Category Archives: matrix computations

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

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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

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1980s Microcomputers and the LINPACK Benchmark

As an undergraduate and postgraduate student in the early 1980s I owned a Commodore Pet microcomputer and then a Commodore 64. Both came with Basic built into ROM. On booting the machines you were presented with a flashing cursor and … Continue reading

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The Nearest Correlation Matrix

A correlation matrix is a symmetric matrix with unit diagonal and nonnegative eigenvalues. In 2000 I was approached by a London fund management company who wanted to find the nearest correlation matrix (NCM) in the Frobenius norm to an almost … Continue reading

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