[Verse 1]
Eigenvalues dance through equations of time
Stability whispers in differential rhyme
Dynamical systems pulse with their beat
While quantum mechanics makes theory complete
Google's PageRank follows their lead
Matrix signatures plant every seed
[Chorus]
Fifteen connections blazing forward now
Spectral theorem shows us how
SVD cuts through data's maze
Linear paths through algebraic haze
Connections forward, pathways bright
Mathematics weaving left and right
[Verse 2]
Spectral theorem splits the light apart
Functional analysis claims its art
Operators dancing in quantum space
Hilbert dimensions find their place
Inner products sing Fourier's song
Signal processing carries along
[Chorus]
Fifteen connections blazing forward now
Spectral theorem shows us how
SVD cuts through data's maze
Linear paths through algebraic haze
Connections forward, pathways bright
Mathematics weaving left and right
[Verse 3]
Singular values decompose the scene
Machine learning's most trusted machine
Dual spaces twist through forms unknown
Cohomology seeds freshly sown
Representation theory takes the stage
Differential forms turn every page
[Bridge]
Matrix groups GL and O march in line
Unitary SL keeping perfect time
Lie algebras wait at course nine's door
Linear transformations show what's in store
Homomorphisms echo through the hall
Prototypes answering algebra's call
[Chorus]
Fifteen connections blazing forward now
Spectral theorem shows us how
SVD cuts through data's maze
Linear paths through algebraic haze
Connections forward, pathways bright
Mathematics weaving left and right
[Outro]
From eigenvalues to groups that transform
Every connection breaks the norm
Path two algebra opens every gate
Fifteen bridges seal our fate