§ Linear Algebra

Topics

Foundations of linear algebra

• Vector spaces and ring modules
• Linear combinations and spanning
• Linear independence
• Vector bases and dimension

Foundations of linear maps

• Linear maps
• Image and kernel
• Compositions and invertible linear maps
• Different perspectives of matrices
• Composition and matrix multiplication

Theorems:

• (Theorem) Rank-nullity
• (Theorem) Invertible matrix

Inner products, orthogonality, and the spectral theorem

• Inner product spaces