Monthly Archives: September 2020

What Is a Householder Matrix?

A Householder matrix is an orthogonal matrix of the form It is easily verified that is orthogonal (), symmetric (), involutory ( that is, is a square root of the identity matrix), where the last property follows from the first … Continue reading

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What is a Sparse Matrix?

A sparse matrix is one with a large number of zero entries. A more practical definition is that a matrix is sparse if the number or distribution of the zero entries makes it worthwhile to avoid storing or operating on … Continue reading

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What Is the Sylvester Equation?

The Sylvester equation is the linear matrix equation where , , and . It is named after James Joseph Sylvester (1814–1897), who considered the homogeneous version of the equation, in 1884. Special cases of the equation are (a standard linear … Continue reading

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