Definitions
===========


The matrix of a linear map

The matrix of a vector

Operator

Injectivity, surjectivity, invertibility of an operator

Inverse map

Isomorphic spaces

Invariant subspaces

Eigenvalues and eigenvectors


Polynomials of operators (operator polynomials)

Matrix of an operator

Upper-triangular and diagonal matrices

Eigenspaces

Diagonalizable operators



Things without proofs
=====================

Thms 3.25, 3.36, 3.38, 3.47, 3.52, 3.60, 3.64 (misprint in the book),

All the theorems of Chapter 4, without proofs

Thms 5.26, 5.27, 5.30, 5.44.


Things that require proofs (theorems, propositions, lemmas)
===========================================================
(You are NOT required to remember theorems, lemmas, and propositions by
their number in the book)

Thms 3.22, 3.23, 3.24, 3.26, 3.54, 3.56, 3.59, 3.65, 3.69,
5.6,  5.10, 5.13, 5.20, 5.21, 5.32, 5.41