Uncertainty's Edge

HTML "3b1b Linear Algebra Quotes"

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This post, A, includes the content of Grant Sanderson's quotes, and B, tests Eleventy's MD & HTML preprocessing

These quotes are from The Essence of Linear Algebra by Grant Sanderson.

Chapter 0: Essence of linear algebra preview

There is hardly any theory which is more elementary than linear algebra, in spite of the fact that generations of professors and textbook writers have obscured its simplicity by preposterous calculations with matrices.

-Jean Dieudonn'e

Chapter 1: Vectors, what even are they?

The introduction of numbers as coordinates is an act of violence.

-Hermann Weyl

Chapter 2: Linear combinations, span, and basis vectors

Mathematics requires a small dose, not of genius, but of an imaginative freedom which, in a larger dose, would be insanity.

-Angus K. Rodgers

Chapter 3: Linear transformations and matrices

Unfortunately, no one can be told what the Matrix is. You have to see it for yourself. [Surprisingly apt words on the importance of visualizing matrix operations.]

-Morpheus

Chapter 4: Matrix multiplication as composition

It is my experience that proofs involving matrices can be shortened by 50% if one throws the matrices out.

-Emil Artin

Chapter 5: Three-dimensional linear transformations

LISA: Well, where's my dad? FRINK: Well, it should be obvious to even the most dimwitted individual who holds an advanced degree in hyperbolic topology that Homer Simpson has stumbled into...[dramatic pause]...the third dimension.

-The Simpsons

Chapter 6: The determinant

The purpose of computation is insight, not numbers.

-Richard Hamming

Chapter 7: Inverse matrices, column space and null space

To ask the right question is harder than to answer it.

-Georg Cantor

Chapter 8: Nonsquare matrices as transformations between dimensions

On this quiz, I asked you to find the determinant of a 2x3 matrix. Some of you, to my great amusement, actually tried to do this.

-Anonymous Professor

Chapter 9: Dot products and duality

CALVIN: You know, I don't think math is a science, I think it's a religion. HOBBES: A religion? CALVIN: Yeah. All these equations are like miracles. You take two numbers and when you add them, they magically become one new number! No one can say how it happens. You either believe it or you don't.

-Calvin & Hobbes

Chapter 10: Cross products

From [Grothendieck], I have also learned not to take glory in the difficulty of a proof: difficulty means we have not understood. The idea is to be able to paint a landscape in which the proof is obvious.

-Pierre Deligne

Chapter 11: Cross products in the light of linear transformations

Every dimension is special.

-Jeff Lagarias

Chapter 12: Cramer's rule, explained geometrically

JERRY: Ah, you're crazy! KRAMER: Am I? Or am I so sane that you just blew your mind? JERRY: It's impossible! KRAMER: Is it?! Or is it so possible your head is spinning like a top?

-Seinfeld

Chapter 13: Change of basis

Mathematics is the art of giving the same name to different things.

-Henri Poincar'e

Chapter 14: Eigenvectors and eigenvalues

Last time, I asked: "What does mathematics mean to you?", and some people answered: "The manipulation of numbers, the manipulation of structures." And if I had asked what music means to you, would you have answered: "The manipulation of notes"?

-Serge Lang

Chapter 15: A quick trick for computing eigenvalues

I'm assuming you know what eigenvalues are. Not This!

-Pi Creature

Chapter 16: Abstract vector spaces

Such axioms, together with other unmotivated definitions, serve mathematicians mainly by making it difficult for the uninitiated to master their subject, thereby elevating its authority.

-Vladmir Arnold