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

Inner product with the properites required by the definition

Norm (induced by the inner product)

Orthogonal decomposition

Orthonormal bases

Projection, orthogonal projection

Gram-Schmidt procedure

Orthogonal compliment

Linear functional

Adjoint (linear map)

Self-adjoint operator

Normal operator


Theorems and other things without proofs
========================================
6.7, 6.10, 6.14, 6.18, 6.22, 6.28, 6.30,
6.34, 6.35, 6.38, 6.46, 6.47, 6.50, 6.51,
6.55, 7.5, 7.10, 7.14, 7.16, 7.20, 7.21,
7.26, 7.28, 7.29


Theorems with proofs
====================
6.13, 6.15, 6.25, 6.26, 6.31, 6.37, 6.42,
6.56, 7.5, 7.7, 7.13, 7.15, 7.22, 7.24, 7.27