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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
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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
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 twopage 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
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