# Category Archives: matrix computations

## Who Invented the Matrix Condition Number?

The condition number of a matrix is a well known measure of ill conditioning that has been in use for many years. For an matrix it is , where is any matrix norm. If is singular we usually regard the … Continue reading

## Empty Matrices in MATLAB

What matrix has zero norm, unit determinant, and is its own inverse? The conventional answer would be that there is no such matrix. But the empty matrix [ ] in MATLAB satisfies these conditions: >> A = []; norm(A), det(A), … Continue reading

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## Faster SVD via Polar Decomposition

The singular value decomposition (SVD) is one of the most important tools in matrix theory and matrix computations. It is described in many textbooks and is provided in all the standard numerical computing packages. I wrote a two-page article about … Continue reading

## Numerical Linear Algebra and Matrix Analysis

Matrix analysis and numerical linear algebra are two very active, and closely related, areas of research. Matrix analysis can be defined as the theory of matrices with a focus on aspects relevant to other areas of mathematics, while numerical linear … Continue reading