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∑MathIntermediate

Pseudoinverse (Moore-Penrose)

The Moore–Penrose pseudoinverse generalizes matrix inversion to rectangular or singular matrices and is denoted A⁺.

#pseudoinverse#moore-penrose#least squares+12
∑MathIntermediate

Matrix Norms & Condition Numbers

Matrix norms measure the size of a matrix in different but related ways, with Frobenius treating entries like a big vector, spectral measuring the strongest stretch, and nuclear summing all singular values.

#matrix norm
Intermediate
Advanced
Filtering by:
#condition number
Group:
Linear Algebra
#spectral norm
#frobenius norm
+12
∑MathIntermediate

Positive Definite Matrices

A real symmetric matrix A is positive definite if and only if x^T A x > 0 for every nonzero vector x, and positive semidefinite if x^T A x ≥ 0.

#positive definite#positive semidefinite#cholesky decomposition+11
∑MathIntermediate

Systems of Linear Equations

A system of linear equations asks for numbers that make several linear relationships true at the same time, which we compactly write as Ax = b.

#systems of linear equations#gaussian elimination#row echelon form+12