Jocko Homomorphism - Diagonal Zeal (SHADOW)

from SpinTunes 17 Round 4 by Spintunes

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about

One of the unsung struggles in mathematics is learning how to spell the vocabulary. There are some easter eggs in this song for students of linear algebra, but this is intended for a general audience. You should come away with the knowledge that diagonalizable is a real word, and have the spelling down to boot.

Spelling is especially pertinant in linear algebra, because the order of variables in an equation changes the result. The technical term is that matrix multiplication is noncommutative, but that's a word for another song.

Diagonal matrices are some of the best behaved, but diagonalizable matrices are a close second. A diagonal matrix A satisfies the (equivalent) equations

B D B^(-1) = A
B^(-1) A B = D,

where D is a diagonal matrix. The formula assumes that B is an invertible matrix, that is

I = B^(-1) B.

The identity matrix I is the equivalent of multiplication by 1 in this context. Not all matrices have inverses.

Including the names of letters, this song has exactly twenty five unique words on the lyric sheet. This allows me to spell out the equations, the word diagonalizable, and even some bonus words that would otherwise put the song over the twenty five word limit. I get another bonus word by using a title which is not a lyric of the song. All of the variable names and bonus words are spelled with letters from diagonalizable.

lyrics

Matrix algebra is hell
Cause I never learned to spell
It's unrecognizable
Diagonalizable
B D B inverse equals A

Diagonal matrix D
I equals B inverse B
It's unrecognizable
Diagonalizable
B inverse A B equals D

D I A G O N A
L I Z A B L E

D I A G O N A
L I Z A B L E

B L I N D E D
E L I D I N G
It's unrecognizable
Diagonalizable
A G O N I Z E D

D I A G O N A
L I Z A B L E

D I A G O N A
L I Z A B L E

credits

from SpinTunes 17 Round 4, released April 25, 2021

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