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Monthly Archives: August 2020
What is the Kronecker Product?
The Kronecker product of two matrices and (also called the tensor product) is the matrix1 In other words, is the block matrix with block . For example, Notice that the entries of comprise every possible product , which is not … Continue reading
What Is the Gerstenhaber Problem?
When Cayley introduced matrix algebra in 1858, he did much more than merely arrange numbers in a rectangular array. His definitions of addition, multiplication, and inversion produced an algebraic structure that has proved to be immensely useful, and which still … Continue reading
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What Is a Cholesky Factorization?
The Cholesky factorization of a symmetric positive definite matrix is the factorization , where is upper triangular with positive diagonal elements. It is a generalization of the property that a positive real number has a unique positive square root. The … Continue reading
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What is Numerical Stability?
Numerical stability concerns how errors introduced during the execution of an algorithm affect the result. It is a property of an algorithm rather than the problem being solved. I will assume that the errors under consideration are rounding errors, but … Continue reading
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