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QRDecomposition

QRDecomposition[m]
yields the QR decomposition for a numerical matrix m. The result is a list {q, r}, where q is an orthogonal matrix and r is an upper-triangular matrix.

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The original matrix m is equal to Conjugate[Transpose[q]].r. »

For non-square matrices, q is row orthonormal. »

The matrix r has zeros for all entries below the leading diagonal. »

QRDecomposition[m, Pivoting->True] yields a list {q, r, p} where p is a permutation matrix such that m.p is equal to Conjugate[Transpose[q]].r. »

EXAMPLES

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Basic Examples (2)

Compute the QR decomposition for a 3×2 matrix with exact values:

Compute the QR decomposition for a 2×3 matrix with approximate numerical values:

Scope (2)

Options (1)

Applications (1)

Properties & Relations (1)