Theorems and proofs

Eigenvalues of linear transformation and representation matrix lemma

Cayley-Hamilton theorem theorem

Diagonalization and minimal polynomial theorem

Pythagorean theorem theorem

Cauchy-Schwarz inequality lemma

Riesz Representation theorem theorem

Existence and uniqueness of adjoint linear transformation theorem

Representation matrix of adjoint linear transformation lemma

Gram-Schmidt matrix of two bases lemma

Polar norm equations lemma

Normal linear operator criterion theorem