Base

condition_number(A)

Find the condition number of matrix, A.

Notes

Definition [burdenNumericalAnalysis2016]_: The condition number of the non-singular matrix, $\mathbf{A}$ relative to a norm, ||⋅|| is

\[ K(\mathbf{A}) = ||\mathbf{A}|| ⋅ ||\mathbf{A}^{-1}||\]

A matrix is well-conditioned if $K(\mathbf{A})$ is close to 1 and is ill-conditioned if significantly greater than 1.

diagonality(A)

Determines whether matrix, A is strictly, diagonally dominant.

positive_definite(A)

Determines whether matrix, A is positive definite.

spectral_radius(A)

Finds the spectral radius of matrix, A.

Notes

$ρ(\mathbf{A}) = \max|λ|$, where λ is the set of eigvalsvalues for A [burdenNumericalAnalysis2016]_.

symmetry(A)

Determines whether matrix, A is symmetric.

tridiagonality(A)

Determine whether matrix, A is tridiagonal.