#eigenvalues

[dnieperrobot69420]

Taking a slight tangent from classical optics, I decided to delve more into non-linear optics.

As someone who never had to use Gaussian form of Maxwell's equations, never used Tensors, and had never used Einsteins notation for summation; let me just say the algebra of the book proved to be a hard nut to crack!

What am I learning about? Anisotropy! Who knew that the direction at which you observe/propagate through a material such as a crystal plays a role in the material properties you will experience!!

I still don't believe you can determine eigenvalues and eigenvectors for an arbitrary 3x3 permittivity matrix (I need to use numerical examples to really see it) and that there exists rotational matricies that let us make the math all neat and proper.

But, slowly and with growing pains, I am continuing to slowly tread the waters of this fascinating topic!

[peeterjoot]

Eigenvalues of 2x2 matrix: another identity seen on twitter.

[Click here for a PDF version of this post] Here��s another interesting looking twitter math post, this time about 2×2 matrix eigenvalues: Theorem 1.1: Eigenvalues of a 2×2 matrix. Let \( m \) be the mean of the diagonal elements, and \( p \) be the determinant. The eigenvalues of the matrix are given by \begin{equation*} m \pm \sqrt{ m^2 – p }. \end{equation*} This is also not hard to…

[mothpdf]

statistics makes me miss calculus

[abalidoth]

broke: I was sold to One Direction

woke: I was sold one direction

theyre selling WHAT on ebay now

[i-iii-iii-vii]

[sparkofthetelling]

my quantum mechanics professor: "a good quantum number is one that conserves with the hamiltonian"

me, woke, tumblr user: "what if we just didn't moralize quantum numbers and described them simply by their properties"

[stopmyhearts]

At some point in the last few weeks this math has turned from weird equations to magic incantations

[anumberofcatschilling]

[Image Description: a section from an article on Wikipedia about lambda, which reads,

In 1970, graphic designer Tom Doerr selected the lower-case Green letter lambda (lowercase lambda) to be the symbol of the New York chapter of the Gay Activist Alliance. The alliance's literature states that Doerr chose the symbol specifically for its denotative meaning in the context of chemistry and physics: "a complete exchange of energy--that moment or span of time witness to absolute activity".

The lambda became associated with gay liberation, and in December 1974, it was officially declared the international symbol for gay and lesbian rights by the International Gay Rights Congress in Edinburgh, Scotland. The gay rights organization Lambda Legal and the American Lambda Literary Foundation derive their names from this symbol

To the right is an image of the lower-case lambda with the caption, "Lower-case lambda"

/. End ID]

As of June 24th, 2024, you can find this section on the Wikipedia page for LGBT symbols.

Happy pride month chat remember that the lambda is an official symbol of gay and lesbian liberation. Goodnight

[laz-ofthestars]

DAAAMN LINEAR ALGEBRA IS SICK

[eternalsnare]

You enjoyed flaunting it, Did you not~?

That adorable little brain of yours, all smug and quick, throwing around proofs and solving equations like it was nothing as if it made you special.

You were mid-sentence, some tangent about eigenvalues or some dirt like that, and I just tilted my head and whispered “Blank now.”

Just like that… it all started to slip

All the little cute symbols on the page stopped making sense first. You blinked, tried to reread them, but they just floated away, like leaves in the summer breeze~ Twisted into nonsense.

Next~ you forgot what the equation meant. What were you even trying to explain, little one~? You don't know. It's all just… Gone.

That gentle panic in your eyes as you realised what I took away, the power I hold over you~

Delicious. And now… look at you~ Mouth parted, Eyes foggy, trying so, so, so hard to hold onto something that isn't yours anymore.

You don’t get to be both clever and obedient. Hehe~ No… You get to kneel. You get to drool. You get to forget.

And next time, you feel like flaunting silly words like ‘vector’ or ‘matrix’ around like you are some kind of smart pet, you will feel that same sweet blankness drippingg into your mind~ Tugging you down.

deeep, deep down Into the lovely, helpless quiet where all your silly little thoughts belong…

With me~

[xoxocher]

𝐒𝐓𝐔𝐃𝐘 𝐁𝐑𝐄𝐀𝐊 𝜗𝜚. ݁₊

SUMMARY -  chris hartley shows up every time you call—no matter how late it is or how flimsy your excuse. he still thinks he’s just helping you pass chemistry. tonight, you’re more than willing to show him just how much you appreciate his dedication.

PAIRING/SETTING - fem!reader x tutor!chris hartley. no prank au. college au. no use of y/n. 

WARNINGS - graphic sexual material (love a good bj), strong language, and chemistry (literal).

W/C - 1,758

A/N - sorry this took for-fucking-ever! anyhoo, here's another love letter to my chris girlies ♥︎ (p.s. to my lovelies sending me requests, i pinky swear that i will get around to answering them, so please hang in there!) btdubs, my taglist and general writing masterlist are up and running!! check my navigation for more info :)

it’s nearing midnight. your room is dim, lit only by the soft yellow cast of a desk lamp and the muted glow from the streetlight outside your window. the remnants of a burnt out candle linger in the air. everything feels hushed. suspended.  

the silence is broken by a gentle knock at the door. you shuffle across the carpet, your pulse thrumming with excitement as you reach for the handle. 

chris stands with his backpack slung carelessly over one shoulder, nose warmed with a subtle blush from the crisp fall air, greeting you with a tender, tight-lipped smile. one that melts the quiet chill of your apartment. 

“hey,” he mutters softly, slipping inside and closing the door behind him. there’s a tiredness in his eyes–a testament to the unreasonable hour–but he’s here, because you called. 

“hi” you echo, stepping aside to let him in. “didn’t wanna bother you this late, but i just…i can’t seem to wrap my head around this shit.”

his expression softens. “you’re never a bother.” 

you pad back to your bedroom. he drops his bag at the foot of the bed, toeing off his scuffed sneakers before settling beside you. he shrugs off his jacket and bends down to rummage through his belongings.

“you know,” he starts, “you don’t have to make up excuses. if you wanted to see me, you could’ve just said so.”

his forwardness catches you off guard.

he chuckles under his breath. “i’m kidding. mostly.”

but the truth was there, unspoken. 

and he had come running, like always.

“here,” he says, leaning closer, the faint scent of cedar and detergent clinging to his skin. “let’s see if we can make some sense of this.”

chris shuffles through his notes, the soft scratch of pen on paper filling the room. you pretend to study the scrawled diagrams and equations on the page, but in truth, you’ve been too busy studying him: the way his bottom lip pulls between his teeth as he considers his words, the flex of his forearms as he steadies the notebook against his thigh. 

“so, when you’re dealing with molecular orbital theory, you have to remember the principles of constructive and destructive interference-” he rambles on, tracing over each wave and shape to emphasize his point. 

he glances up at you to check for understanding. “so if…um, do you…you’re following this?”

you shake your head, forcing your gaze to meet his. “uh yeah, totally. all good.” you bite at the inside of your cheek, your tone more hopeful than convincing.

he squints at you, “sure you’re okay? you’ve been kinda…spacey.”

you perk up at his accusation, “sorry, just…processing.”

his thumb rolls at the paper’s edge. “i can go over it again if you want…or we could just take a break? i mean, if you’re done for the night i wouldn’t blame-” 

you wave him off, “no, no–continue. talk nerdy to me.” 

he clears his throat, cheeks coloring slightly. “o-okay, just slow me down if it’s too much.”

the sincerity in his voice tugs at your heartstrings.

“so, if we’re calculating the energy levels, you use the secular determinant to find the eigenvalues—those correspond to the molecular orbital energies-”

you nod along, but his words continue to blur together–each one melting into the next until they’re background noise against the louder pull of your wandering thoughts.

you have to cut in.  

“you’re really patient with me, you know that?”

he pauses, pen hovering over the paper to shoot you a curious look. 

“wh-what?”

you lean back on your hands, head tilting slightly as you study him in the low, warm light of your bedroom. his brow is furrowed, glasses sliding down the bridge of his nose, hair falling forward like it always does when he’s too focused to fix it.

“you’ve been sitting here for an hour. no complaints. not even when i give you that stupid, blank look.”

he ducks his head a little, bashfully rubbing the back of his neck. “you asked for help. just doing my job.”

“i ask for help a lot,” you point out, lips quirking. “and it’s not exactly ‘a job’ if you aren’t being compensated.”

you think back to the handful of times you’d offered–cash, coffee, dinner, anything. but he’d always refuse with that same boyish smile, that same small shake of the head like the idea of taking anything from you felt wrong. like your time was worth more than his. and he never let you push the issue. 

too kind. too stubborn. too chris.

“just saying,” you shrug, “kiiinda feels like i’m using you.”

“i don’t mind,” he interjects. “seriously. it’s not a big deal–i want you to pass. and–uh–it’s kinda nice. being needed, i guess.” his voice trails off at the end, sheepish.

you cock your head at him, unconvinced.

“yeah? you do this for your other clients?” 

he begins rapidly tapping his pen against his notebook, eyes darting to the page like it might offer him an escape route. “well no, i don’t really have time for anyone else, but that’s not-”

you roll your eyes with a loud, almost theatrical scoff.

“god, you’re too good to me,” you reach across the space between you and place your hand gently atop his, stilling the frantic motion of his pen.“ and i don’t think i’ve properly thanked you.”

he opens his mouth—probably to deflect, to assure you that it’s nothing, or you don’t owe him anything—but the words die on his tongue when your hand comes up to cup his jaw.

“come on chrissy,” you coax, playfully pinching his chin between your fingers. “let me take care of you.”

the anxious little scrunch between his brows lingers for a beat longer, but he doesn’t pull away, doesn’t protest. he stays still–watching you, trusting you–even as you rise to your knees and shift into his lap, your thighs straddling his. your fingers find their way in the mess of his hair, threading through the tousled strands. then, you carefully adjust his glasses, fingers coming down to cradle his face, before pressing your lips to his. 

a moment of sweet fragility. 

 his fingers drift like leaves on an autumn breeze, too afraid to settle. but every drag of his mouth over yours, a slow burn that leaves you both aching for more, draws him further out of his own head and into the moment, into you.

what starts as soft and uncertain quickly melts into something far less innocent–hunger born where hesitation once lingered. his breath shudders against your lips as he holds you tighter, the world falling away in the delicious, heady rhythm of tongue and teeth. 

you part from his mouth with a sigh, but you don’t stray far–trailing your lips down the pale stretch of his throat to lightly nip at the delicate skin. a low, needy whimper slips past his lips as you roll your hips over the swell in his jeans. 

“jesus,” he pants, voice frayed with disbelief and arousal. “you’re gonna kill me.”

you giggle at his flustration. “not yet,” you tease.

you sink to the floor, fingers deft on the button of his jeans. you ease the denim down along with his boxers, savoring the hitch in his breath as you peel everything away. his cock springs free, tapping softly against his stomach–thick, flushed, and glistening at the tip. you can’t help but stare. 

no one’s dick should be this pretty. 

you wrap your fingers around him, featherlight at first. he twitches in your grasp, and you watch, transfixed, as your thumb swipes over his head, smearing the small beads of precum. you stroke him once, then again, slow and sure, relishing in his reaction—his thighs tensing, a sharp exhale cutting through the thick silence of your bedroom. 

“are you–ah~s-sure? you don’t have t–” 

you answer not with words but action, leaning in to lick a single, deliberate stripe up the underside of his cock. he jolts forward, head tipping back as your lips part around him. 

when you lift your gaze to meet his–eyes wide and glassy–his mouth falls open in a silent gasp, undone by the sight of you on your knees for him. his hands fist the sheets at his sides, knuckles white, chest rising in uneven breaths. 

“h-holy shit. o-okay yeah, you’re sure. i get it.” 

your mouth works him steadily, cheeks hollowing as your tongue traces along each pulse with flat, firm strokes. you can’t take all of him–the stretch making your jaw ache–but you give what you can. your hand–slick with the drool that drips down your chin and pools at his base–pumps what you can’t quite fit. 

you take his hand, guiding it to your hair, anchoring him there. his fingers curl in the strands, tugging ever so slightly as his hips instinctively buck upward. you hum around him in approval, the vibration pulling a ragged moan from his chest. and when your free hand drifts between your legs, you don’t bother hiding it–dipping down into your panties to soothe your own ache–but chris certainly doesn’t mind.

“fu-uuck you’re unreal.” 

sweat begins to collect in a thin sheen across his forehead, lashes fluttering as his eyes roll back into his skull. 

oh what a beautiful mess you’ve made of this man. 

even now, he’s gentle—or trying to be, at least–slowing his thrusts to mutter sweet little apologies every now and then. but when he inevitably hits the back of your throat, you feel a sting at the corners of your eyes. you blink through it, tears trailing down your cheeks as you take him deeper, sinking into the pain. his soft, broken whines–like music to your ears–are all the motivation you need.

“ungh~gonna–mph–cum.”

his release is sudden and overwhelming. warm ropes of cum shoot down your throat in thick waves that leave him shaking and slack-jawed. you swallow him down, milking every last drop, before coming up to place a few kisses and kitten licks to his sensitive tip. he hisses at the overstimulation, already shuddering in the aftershock. 

you carefully tuck him back into his boxers and crawl up into his lap, licking over your lips before planting a lazy kiss on his. it’s slow and sticky, his taste still lingering on your tongue as you part his lips and let him share it. he groans low and warm against your mouth, breath gradually slowing as his high fades.

“think you broke my brain.” he huffs with a dopey grin.  “good,” you beam, gently patting his cheek. “you’ve been using it too hard.”

© 2025 xoxocher | don’t copy, repost, or translate my work

taglist: @bongwaterbunny

[wu-sisyphus-gang]

Dr. Polendina: Your friend Mr Arc is incredibly frustrating.

Penny: How so?

Dr Polendina: He will sketch a proof of the grand Riemann conjecture using eigenvalues of a quantum theory of spin and then stop and ask me if snow can cure cancer. He will be in his flow and almost prove an isomorphism between the sphere in infinite dimensions and the schrodinger equation and stop and then say 'its too late, I'm already in my pyjamas'.

Penny: Weren't you going to explain to him how you solved the hard problem of consciousness and then said here's the wire I used?

Pietro: It's okay when I do it!

[misspepeshi]

Get to Know You/Catch Up Tag ✨

Thank you for the tag, @edmunderson! 💛

📖 Currently reading: Daredevil: To Heaven Through Hell, and Heaven Official’s Blessing!

🎶 Last song I listened to: She Is Beautiful by Andrew W.K. I’ve been listening to this song a little bit too much! 🥲

📺 Last series: Outer Range. I have to take breaks with this one. The episodes always leave my brain overwhelmed.

🎞️ Last movie: McFarland, USA.

📺 Currently watching: My Deer Friend Nokotan and The Master of Diabolism. I love, LOVE, Nokotan. 🦌

🍱 Sweet/Savoury/Spicy: 50% sweet, 50% savoury. ¿? Unfortunately I have IBS and cannot tolerate well sugary and/or spicy food anymore.

❤️ Relationship status: In a relationship with Mister Pepeshi, who isn’t Pepeshi-sized at all. 😆

🖌️ Favorite color: I’ve always pondered on this. What color does truly define me? Black, Purple, and Royal Blue. ¿?

🫡 Current obsession: Chicken sandwiches with no pickles……… and wanting to make a Caribbean, sun-kissed, green or turquoise-eyed, light/dark brown hair sim. With nice legs and booty. A tropical-esque occult. ¿? Second one will have to wait.

🫖 Tea or Coffee: Chocolate milk! 🤠

❔Last thing I Googled: What Linear Algebra is used for within your career path. 🫠 Lovely, lovely eigenvectors, eigenvalues, matrices……… *brain combusts*.

Tagging: @aching-joints, @bloody-soda, @herzblau, @itawdoris, @kagumiya, @strangegrapefruit. 🌼

As always, you don’t have to do it if you don’t want to!

[mindblowingscience]

Is it possible to deduce the shape of a drum from the sounds it makes? This is the kind of question that Iosif Polterovich, a professor in the Department of Mathematics and Statistics at Université de Montréal, likes to ask. Polterovich uses spectral geometry, a branch of mathematics, to understand physical phenomena involving wave propagation. Last summer, Polterovich and his international collaborators—Nikolay Filonov, Michael Levitin and David Sher—proved a special case of a famous conjecture in spectral geometry formulated in 1954 by the eminent Hungarian-American mathematician George Pólya. The conjecture bears on the estimation of the frequencies of a round drum or, in mathematical terms, the eigenvalues of a disk.

Continue Reading.

[schrodingers-redfish]

Girl help, there are imaginary numbers in my matrices in my differential equations

Starting a new trend to counteract "I'm just a girl" culture

[stargazerbibi]

[ 25th november, 2024 • 78/152 days ]

very difficult day, but i think i won in the end. read a post (link below) about shame/guilt being demotivators and finally understood what "you can't shame yourself into being productive" means. i think it applies to the majority of things in my life so i want to journal about it soon

-> classes (total: 6h30)

-> studied for the AL test + quick notes (CR factorisation, base transformations, eigenvalues and eigenvectors, Jordan)

-> AL worksheet 6 (total: 1h00 - complete ☑️)

-> AL worksheet 7 (total: 1h30 - 50%)