= Both the formula for ordinary matrix multiplication and the Cauchy–Binet formula for the determinant of the product of two matrices are special cases of the following general statement about the minors of a product of two matrices. Where ‘I’ is the identity matrix, A-1 is the inverse of matrix A, and ‘n’ denotes the number of rows and columns. Matrix Multiplication. We can get the orthogonal matrix if the given matrix should be a square matrix. The cofactor is preceded by a + or – sign depending whether the element is in a + or – position. ≤ (where the In this article, we use the inclusive definition of choosing the elements from rows of I and columns of J. The complement, Bijk...,pqr..., of a minor, Mijk...,pqr..., of a square matrix, A, is formed by the determinant of the matrix A from which all the rows (ijk...) and columns (pqr...) associated with Mijk...,pqr... have been removed. The cofactors feature prominently in Laplace's formula for the expansion of determinants, which is a method of computing larger determinants in terms of smaller ones. All identity matrices are an orthogonal matrix. ) i p {\displaystyle 1\leq i_{1}
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