Matrix Norm Calculator

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Choose the number of rows and columns. Supported up to 4x4.
Element at row 1, column 1.
Element at row 1, column 2.
Element at row 1, column 3.
Element at row 1, column 4.
Element at row 2, column 1.
Element at row 2, column 2.
Element at row 2, column 3.
Element at row 2, column 4.
Element at row 3, column 1.
Element at row 3, column 2.
Element at row 3, column 3.
Element at row 3, column 4.
Element at row 4, column 1.
Element at row 4, column 2.
Element at row 4, column 3.
Element at row 4, column 4.
Frobenius NormLarge magnitude
14.2478

sqrt of the sum of all squared entries, the most commonly used matrix norm

1-Norm (max column sum)16
Infinity Norm (max row sum)15
Spectral 2-Norm13.0816
Max Norm9
Frobenius14.2478
1-Norm16
Inf-Norm15
Spectral13.0816
Max9

Frobenius norm: 14.2478

  • The spectral (2-)norm is 13.0816, which equals the matrix's largest singular value and bounds how much it can stretch a unit vector.
  • The 1-norm (16.0000) and infinity norm (15.0000) bound the spectral norm from above: spectral norm is always at most min(1-norm, inf-norm).
  • This is a 3x3 square matrix. The Frobenius norm satisfies ||A||_F >= ||A||_2 >= ||A||_max >= 0 for any matrix.

Next stepTo estimate the condition number of a square matrix, divide the spectral norm of A by the spectral norm of A^(-1). A condition number near 1 means the system is well-conditioned.

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