Determinant

Shipping

matrix_determinant

Scalar determinant det(A) via MKL LAPACK; dimensionless

Signature

Inputs

aSignal|Arrayrequired— A square 2-D matrix.

Outputs

determinantScalar— The scalar determinant $\det A$ (dimensionless).

Description

Determinant returns the scalar $det A$ of a square matrix, computed through the MKL LAPACK backend (an LU factorization internally). It measures the signed volume scaling of the linear map and vanishes exactly when $A$ is singular.

The input is read as a 2-D matrix; the result is a dimensionless Scalar. For large matrices whose determinant would overflow or underflow the floating-point range, prefer matrix_slogdet, which returns the sign and the log of the absolute value separately and stays numerically well-behaved.

Mathematics

det A = σ \sum sgn (σ) i \prod A_{i, σ (i)}

A is invertible ⟺ det A \neq = 0

Examples

2×2 determinant

For $A = [4276]$ , the determinant output is $4 \cdot 6 - 7 \cdot 2 = 10$ .

Applications

Testing invertibility / singularity before a solve or inverse.
Computing signed volume scaling (Jacobian determinants) in change-of-variables and geometry.
Checking orientation preservation of a transform (sign of the determinant).

Neat

It shares the same LU machinery as the solver family, so determinant, solve, and inverse are numerically consistent about singularity.

For values that would overflow, matrix_slogdet exposes the log-domain path used internally, avoiding $\pm\infty$ readings.

Known issues

For large or poorly scaled matrices the determinant can overflow or underflow to $0$/$\infty$; use matrix_slogdet instead.

A near-zero determinant does not by itself quantify conditioning — use matrix_cond for that.