Monthly Archives: June 2020

What Is the Hilbert Matrix?

The Hilbert matrix is the matrix with . For example, It is probably the most famous test matrix and its conditioning and other properties were extensively studied in the early days of digital computing, especially by John Todd. The Hilbert … Continue reading

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What Is a Fréchet Derivative?

Let and be Banach spaces (complete normed vector spaces). The Fréchet derivative of a function at is a linear mapping such that for all . The notation should be read as “the Fréchet derivative of at in the direction ”. … Continue reading

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Six Useful LaTeX Packages

Here are six packages that, while they are perhaps not among the best known, I have found to be very useful. All of them are probably available in your distribution, but in case they are not I give links to … Continue reading

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What Is the Adjugate of a Matrix?

The adjugate of an matrix is defined by where denotes the submatrix of obtained by deleting row and column . It is the transposed matrix of cofactors. The adjugate is sometimes called the (classical) adjoint and is sometimes written as … Continue reading

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What Is a Matrix Function?

If you give an array as the argument to a mathematical function in a programming language or problem solving environment you are likely to receive the result of applying the function to each component of the array. For example, here … Continue reading

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Randsvd Matrices with Large Growth Factors

Sixty years ago James Wilkinson published his backward error analysis of Gaussian elimination for solving a linear system , where is a nonsingular matrix. He showed that in floating-point arithmetic the computed solution satisfies where is the unit roundoff and … Continue reading

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What Is Bfloat16 Arithmetic?

Bfloat16 is a floating-point number format proposed by Google. The name stands for “Brain Floating Point Format” and it originates from the Google Brain artificial intelligence research group at Google. Bfloat16 is a 16-bit, base 2 storage format that allocates … Continue reading

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