In mathematics, a triangular matrix is a special kind of square matrix. A square matrix is called lower triangular if all the entries above the main diagonal...
21 KB (3,152 words) - 16:41, 28 April 2024
called an upper triangular matrix. Similarly, if all entries of A above the main diagonal are zero, A is called a lower triangular matrix. If all entries...
106 KB (13,096 words) - 09:11, 30 July 2024
the Crout matrix decomposition is an LU decomposition which decomposes a matrix into a lower triangular matrix (L), an upper triangular matrix (U) and,...
3 KB (363 words) - 17:37, 11 May 2020
} Proposition — A normal triangular matrix is diagonal. Proof Let A be any normal upper triangular matrix. Since ( A ∗ A ) i i = ( A A ∗ ) i...
13 KB (1,656 words) - 01:07, 5 June 2024
decomposition. The LU decomposition factorizes a matrix into a lower triangular matrix L and an upper triangular matrix U. The systems L ( U x ) = b {\displaystyle...
26 KB (3,580 words) - 17:05, 12 March 2024
QR decomposition (category Matrix decompositions)
factorization, is a decomposition of a matrix A into a product A = QR of an orthonormal matrix Q and an upper triangular matrix R. QR decomposition is often used...
28 KB (4,632 words) - 10:32, 19 July 2024
LU decomposition (category Matrix decompositions)
or factorization factors a matrix as the product of a lower triangular matrix and an upper triangular matrix (see matrix decomposition). The product...
39 KB (6,244 words) - 03:24, 13 August 2024
positive definiteness of a symmetric real matrix. Namely, the matrix is reduced to an upper triangular matrix by using elementary row operations, as in...
50 KB (8,586 words) - 13:43, 4 August 2024
diagonal matrix. If all entries below (resp above) the main diagonal are zero, A {\displaystyle A} is called an upper (resp lower) triangular matrix. The...
16 KB (1,831 words) - 06:07, 16 June 2024
Schur decomposition (redirect from Schur triangular form)
Schur, is a matrix decomposition. It allows one to write an arbitrary complex square matrix as unitarily similar to an upper triangular matrix whose diagonal...
11 KB (1,360 words) - 15:26, 12 August 2024