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Compute the full QR decomposition of a matrix
ResourceFunction["FullQRDecomposition"][m] yields the full QR decomposition for a numerical matrix m. The result is a list {q,r}, where q is a unitary matrix and r is an upper‐trapezoidal matrix. |
Compute the full QR decomposition for a 3×2 matrix with exact values:
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Compute the full QR decomposition for a 2×3 matrix with approximate numerical values:
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Use a 3×4 matrix:
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Full QR decomposition computed with exact arithmetic:
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Full QR decomposition computed with machine arithmetic:
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Full QR decomposition computed with 24-digit arithmetic:
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Full QR decomposition for a 3×3 matrix with random complex entries:
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Use a 3×4 matrix:
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Compute the full QR decomposition using machine arithmetic with pivoting:
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The elements along the diagonal of r are in order of decreasing magnitude:
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The matrix p is a permutation matrix:
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FullQRDecomposition satisfies m.p==ConjugateTranspose[q].r:
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Here is some data:
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Set up a design matrix for fitting with basis functions 1, t, t2:
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Find the full QR decomposition of m:
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This finds a vector x such that is a minimum:
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These are the coefficients for the least-squares fit:
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Use a 3×4 matrix:
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Compute the full QR decomposition:
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The rows and columns of q are orthonormal:
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Check that r is upper trapezoidal:
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Check that m is equal to ConjugateTranspose[q].r:
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