Pseudoinverse

The Moore–Penrose inverse generalizes matrix inversion to least-squares and rank-deficient problems.

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Quadratic forms
A quadratic form assigns a homogeneous degree-two scalar expression to a vector.
Singular value decomposition
Unitary or orthogonal factors and a rectangular diagonal factor describe any finite matrix.
Basis and dimension
A basis is a linearly independent spanning set; every vector has unique coordinates in that basis.
Condition numbers
A matrix condition number describes sensitivity of linear-system solutions to perturbations.
Determinants
The determinant of a square matrix tracks signed volume scaling and is nonzero exactly when the matrix is invertible.