Mathematics MOC

Linear algebra MOC

Linear algebra is the study of 𝖵𝖾𝖼𝗍𝕂. 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)
• 𝕂-tensor product of vector spaces

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