Mathematics MOC

Linear algebra MOC

Linear algebra is the study of Category of vector spaces. Vector notation in these notes. Linear algebra is generalized by Module theory MOC.

Objects

Vector space

• Span
• Linear (in)dependence
• Vector basis
• Dimension of a vector space

Extra structure

• Quadratic space

Morphisms

• Linear map

In a fixed basis

• Matrix algebra over a field
• Types of square matrix
• Row and column space

Properties of morphisms

• Eigenvectors, eigenvalues, and eigenspaces
• Diagonalization

Internal constructions

• Vector subspace
• Complement subspace

Externally

• Quotient vector space
• Direct product vector space (product), Direct sum of vector spaces (coproduct)
• Tensor product of vector spaces over a field

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