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In mathematics, the determinant is a scalar-valued function of the entries of a square matrix.The determinant of a matrix A is commonly denoted det(A), det A, or | A |.Its value characterizes some properties of the matrix and the linear map represented, on a given basis, by the matrix.
In mathematics, the Weinstein–Aronszajn identity states that if and are matrices of size m × n and n × m respectively (either or both of which may be infinite) then, provided (and hence, also ) is of trace class,
Sylvester's determinant theorem (determinants) Sylvester's theorem (number theory) Sylvester pentahedral theorem (invariant theory) Sylvester's law of inertia (quadratic forms) Sylvester–Gallai theorem (plane geometry) Symmetric hypergraph theorem (graph theory) Symphonic theorem (triangle geometry) Synge's theorem (Riemannian geometry)
The determinant of the left hand side is the product of the determinants of the three matrices. Since the first and third matrix are triangular matrices with unit diagonal, their determinants are just 1. The determinant of the middle matrix is our desired value. The determinant of the right hand side is simply (1 + v T u). So we have the result:
Download as PDF; Printable version; ... Pages in category "Determinants" ... Fredholm determinant; Frobenius determinant theorem; Functional determinant; G.
Download as PDF; Printable version; ... Theorem. The divergence of ... In the 2×2 case, if the coefficient determinant is zero, then the system is incompatible if ...
Download as PDF; Printable version; In other projects Wikidata item; Appearance. move to sidebar hide. Help ... Stein-Rosenberg theorem; Sylvester's determinant identity;
Theorem. (Jacobi's formula) For any differentiable map A from the real numbers to n × n matrices, = ( ()).Proof. Laplace's formula for the determinant of a matrix A can be stated as