HTML "3b1b Linear Algebra Quotes"
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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 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
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