Matrix Decomposition Calculator

Compute LU, QR, SVD, and Cholesky decompositions for square matrices up to 6x6 and report residual checks.

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Save to create a persistent, shareable workspace.

What This Calculator Does

Compute LU, QR, SVD, and Cholesky decompositions for square matrices up to 6x6 and report residual checks.

It combines Matrix Size, a11, a12, a13 to estimate LU Decomposition, LU Residual ||A-LU||_F, QR Decomposition.

Formula & Method

Core equations: A=LU, A=QR (Q orthonormal), A=U\Sigma V^T, and for SPD matrices A=LL^T.

Notation used in the formulas: R = LU Decomposition; x_{1} = Matrix Size; x_{2} = a11; x_{3} = a12; x_{4} = a13; x_{5} = a14; x_{6} = a15.

Method summary: inputs are normalized to consistent units, core equations are evaluated, then secondary values are derived and rounded for display.

Use this calculator for quick scenario analysis. Start with baseline values, change one driver at a time, and compare how sensitive the results are to each input shown above.

Inputs Used

Matrix Size: Used directly in the calculation.
a11: Used directly in the calculation.
a12: Used directly in the calculation.
a13: Used directly in the calculation.
a14: Used directly in the calculation.
a15: Used directly in the calculation.
a16: Used directly in the calculation.
a21: Used directly in the calculation.
a22: Used directly in the calculation.
a23: Used directly in the calculation.
a24: Used directly in the calculation.
a25: Used directly in the calculation.
a26: Used directly in the calculation.
a31: Used directly in the calculation.
a32: Used directly in the calculation.
a33: Used directly in the calculation.
a34: Used directly in the calculation.
a35: Used directly in the calculation.
a36: Used directly in the calculation.
a41: Used directly in the calculation.
a42: Used directly in the calculation.
a43: Used directly in the calculation.
a44: Used directly in the calculation.
a45: Used directly in the calculation.
a46: Used directly in the calculation.
a51: Used directly in the calculation.
a52: Used directly in the calculation.
a53: Used directly in the calculation.
a54: Used directly in the calculation.
a55: Used directly in the calculation.
a56: Used directly in the calculation.
a61: Used directly in the calculation.
a62: Used directly in the calculation.
a63: Used directly in the calculation.
a64: Used directly in the calculation.
a65: Used directly in the calculation.
a66: Used directly in the calculation.

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