the trace equals the sum of eigenvalues: tr(A) = Σλ_i

the determinant tells you about volume scaling under a linear transformation

The determinant of a matrix representing a linear transformation indicates the factor by which volumes are scaled

the dot product measures alignment: it equals |a||b|cos(θ)

Dot product measures alignment: it equals |a||b|cos(θ)

Cholesky decomposition

Cholesky decomposition factors A = LL^T for symmetric positive definite matrices

Eigenvalues and eigenvectors

Eigenvectors are unchanged in direction by a linear transformation

Matrix norm

L1 norm of a vector is the sum of absolute values of its components

Invertible matrix

Rank-nullity theorem: rank(A) + nullity(A) = n