Matrix determinant lemma - Wikipedia
https://en.wikipedia.org/wiki/Matrix_determinant_lemmaStatement. Suppose A is an invertible square matrix and u, v are column vectors.Then the matrix determinant lemma states that (+) = (+) ().Here, uv T is the outer product of two vectors u and v. The theorem can also be stated in terms of the adjugate matrix of A: (+) = + (),in which case it applies whether or not the square matrix A is invertible.. Proof ...
The determinant of the sum of two matrices
www.cambridge.org › core › servicesTHE DETERMINANT OF THE SUM OF TWO MATRICES CHI-KWONG LI AND ROY MATHIAS Let A and B b Xe n n matrices over the real or complex field. Lower and upper bounds for |dei(.A + B)\ are given in terms of the singular values of A and B. Ex-tension of our techniques to estimate \f(A + J5)| for other scalar-valued functions / on matrices is also considered. 1.