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In linear algebra, the Laplace expansion, named after Pierre-Simon Laplace, also called cofactor expansion, is an expression of the determinant of an n × n-matrix B as a weighted sum of minors, which are the determinants of some (n − 1) × (n − 1)-submatrices of B.
Cofactors can be divided into two major groups: organic cofactors, such as flavin or heme; and inorganic cofactors, such as the metal ions Mg 2+, Cu +, Mn 2+ and iron–sulfur clusters. Organic cofactors are sometimes further divided into coenzymes and prosthetic groups. The term coenzyme refers specifically to enzymes and, as such, to the ...
In linear algebra, a minor of a matrix A is the determinant of some smaller square matrix generated from A by removing one or more of its rows and columns. Minors obtained by removing just one row and one column from square matrices (first minors) are required for calculating matrix cofactors, which are useful for computing both the determinant and inverse of square matrices.
In linear algebra, the adjugate or classical adjoint of a square matrix A, adj(A), is the transpose of its cofactor matrix. [1] [2] It is occasionally known as adjunct matrix, [3] [4] or "adjoint", [5] though that normally refers to a different concept, the adjoint operator which for a matrix is the conjugate transpose.
Kirchhoff's theorem can be used to calculate the number of spanning trees for a given graph. The sparsest cut of a graph can be approximated through the Fiedler vector — the eigenvector corresponding to the second smallest eigenvalue of the graph Laplacian — as established by Cheeger's inequality.
Writing the transpose of the matrix of cofactors, known as an adjugate matrix, may also be an efficient way to calculate the inverse of small matrices, but the recursive method is inefficient for large matrices. To determine the inverse, we calculate a matrix of cofactors:
The Dow Jones has lost 1,200 points over the past two days. US stocks sold off on Friday in their worst day of 2025, just two days after the S&P 500 closed at a record high.
Mason's gain formula (MGF) is a method for finding the transfer function of a linear signal-flow graph (SFG). The formula was derived by Samuel Jefferson Mason, [1] for whom it is named.