Abstract: This chapter focuses on adjoint matrices, Hadamard products, the commutation and the duplication matrix, and some results on the bordered Gramian matrix with applications to the solution of certain matrix equations. It discusses that the cofactor c j of the element a j of any square matrix A is ( -1) i+j times the determinant of the submatrix obtained from A by deleting row i and column j . The matrix C = (c j ) is called the cofactor 'matrix of A . The adjoint matrix also appears in the evaluation of the determinant of a bordered matrix. The chapter reviews the general solutions of the matrix equation AX = 0 , where A is an n x n matrix with rank n -1 . The key property of the commutation matrix (and the one from which it derives its name) enables us to interchange (commute) the two matrices of a Kronecker product.
Publication Year: 2019
Publication Date: 2019-02-18
Language: en
Type: other
Indexed In: ['crossref']
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Cited By Count: 2
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