Search results
Results from the WOW.Com Content Network
Adjugate matrix. In linear algebra, the adjugate of a square matrix A is the transpose of its cofactor matrix and is denoted by adj (A). [1][2] It is also occasionally known as adjunct matrix, [3][4] or "adjoint", [5] though the latter term today normally refers to a different concept, the adjoint operator which for a matrix is the conjugate ...
Laplace expansion. 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. Specifically, for every i, the Laplace expansion ...
Conjugate transpose. In mathematics, the conjugate transpose, also known as the Hermitian transpose, of an complex matrix is an matrix obtained by transposing and applying complex conjugation to each entry (the complex conjugate of being , for real numbers and ). There are several notations, such as or , [1] , [2] or (often in physics) .
The name adjoint state method refers to the dual form of the problem, where the adjoint matrix is used. When the initial problem consists of calculating the product and must satisfy , the dual problem can be realized as calculating the product ( ), where must satisfy . And is called the adjoint state vector.
Cramer's rule. In linear algebra, Cramer's rule is an explicit formula for the solution of a system of linear equations with as many equations as unknowns, valid whenever the system has a unique solution. It expresses the solution in terms of the determinants of the (square) coefficient matrix and of matrices obtained from it by replacing one ...
In mathematics, a Hermitian matrix (or self-adjoint matrix) is a complex square matrix that is equal to its own conjugate transpose —that is, the element in the i -th row and j -th column is equal to the complex conjugate of the element in the j -th row and i -th column, for all indices i and j: or in matrix form:
Any block diagonal matrix whose blocks are Jordan blocks is called a Jordan matrix. This (n1 + ⋯ + nr) × (n1 + ⋯ + nr) square matrix, consisting of r diagonal blocks, can be compactly indicated as or , where the i -th Jordan block is Jλi,ni. For example, the matrix is a 10 × 10 Jordan matrix with a 3 × 3 block with eigenvalue 0, two 2 ...
Laplacian matrix. In the mathematical field of graph theory, the Laplacian matrix, also called the graph Laplacian, admittance matrix, Kirchhoff matrix or discrete Laplacian, is a matrix representation of a graph. Named after Pierre-Simon Laplace, the graph Laplacian matrix can be viewed as a matrix form of the negative discrete Laplace ...