Moreover, the inverse of a triangular matrix is also triangular. Also the product of two lower triangular matrices produces a lower triangular matrix, the same apply for upper triangular matrices. A lot of important notions, such as the determinant, the eigenvalue problem and many others are ...
[lower,upper] = bandwidth(A) returns the lower bandwidth, lower, and upper bandwidth, upper, of matrix A. exampleExamples collapse all Find Bandwidth of Triangular Matrix Copy Code Copy Command Create a 6-by-6 lower triangular matrix. Get A = tril(magic(6)) A = 6×6 35 0 0 0 ...
LowerTriangularMatrixQ[m] gives True if m is lower triangular, and False otherwise. LowerTriangularMatrixQ[m, k] gives True if m is lower triangular starting down from the k\[Null]^th diagonal, and False otherwise.
Upper Triangular Matrix Explore with Wolfram|Alpha References Ayres, F. Jr.Schaum's Outline of Theory and Problems of Matrices.New York: Schaum, p. 10, 1962. Referenced on Wolfram|Alpha Lower Triangular Matrix Cite this as: Weisstein, Eric W."Lower Triangular Matrix." FromMathWorld--A Wolfra...
If L'L = U'U, where L and U are lower and upper triangular matrices respectively, then how to get U directly from L? P.S.: I already knew one solution is U = QR (L), but this operation need O(N^3) if L's size is N*N. I am wondering whether there is a O...
As is well known, there exists an invertible matrix S such that S-1AS is upper triangular. The present paper is concerned with the observation that S can always be chosen in the form S=∏L, where ∏ is a permutation matrix and L is lower triangular. Assuming that the eigenvalues of A...
Decomposition of [A] into Lower and Upper Triangular Matrices The given system of equations is (7.1a)[A]X→=b→ The matrix [A] can be written as (7.8)[A]=[aij]=[L][U] where [L] = [lij] is a lower triangular matrix, and [U] = [uij] is a unit upper triangular matrix, ...
I would like to create a matrix of the following structure on a large scale: B=[2 3 4 5 6; 3 4 5 6 0; 4 5 6 0 0; 5 6 0 0 0; 6 0 0 0 0] B =5×5 2 3 4 5 6 3 4 5 6 0 4 5 6 0 0 5 6 0 0 0 6 0 0 0 0 ...
Lower-Middle-Upper Lower-Normandy Lower-Order Path Adaptation Lower-Order Path Termination lower-ranking lower-rankingly lower-sideband upconverter Lower-triangular matrix Lower-Upper-Middle Lower-Voltage Higher Frequency Lower/Upper Alternating Direction Implicit ...
Lower-Middle-Upper Lower-Normandy Lower-Order Path Adaptation Lower-Order Path Termination lower-ranking lower-rankingly lower-sideband upconverter Lower-triangular matrix Lower-Upper-Middle Lower-Voltage Higher Frequency Lower/Upper Alternating Direction Implicit ...