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If the third output P is specified, then L is returned as a unit lower triangular matrix (that is, a lower triangular matrix with 1s on the main diagonal). If the third output P is not specified, then L is returned as a row-permutation of a unit lower triangular matrix. Specifically,...
2.3.1 NOTATION AND TERMINOLOGY We denote a matrix with boldface uppercase letters like this: M or A. Each of the items in a matrix is called an element. The horizontal and vertical arrays of elements (that is, tuples) are called rows and columns, respectively. The numbers of rows and ...
(1.33)[α][k]=[k]-1[k]=[I] where [I] is the unit matrix, a square matrix with all diagonal terms equal to unity, and all other terms zero. Since the stiffness matrix (or the flexibility matrix) relates forces (or moments) applied anywhere on a linear structure to the displacements...
Create a symbolic matrix with the main diagonal specified by the vectorv. syms a b c v = [a b c]; diag(v) ans = [ a, 0, 0] [ 0, b, 0] [ 0, 0, c] Create Matrix with Subdiagonal as Vector Create a symbolic matrix with the second diagonal below the main diagonal specified...
x = diag(A,k)returns a column vector of the elements on thekth diagonal ofA. example Examples collapse all Create Diagonal Matrices Create a 1-by-5 vector. v = [2 1 -1 -2 -5]; Usediagto create a matrix with the elements ofvon the main diagonal. ...
A diagonal matrix is a square matrix of the form (1) where is the Kronecker delta, are constants, and , 2, ..., , with no implied summation over indices. The general diagonal matrix is therefore of the form (2) often denoted . The diagonal matrix with elements can be ...
x = diag(A,k)returns a column vector of the elements on thekth diagonal ofA. example Examples collapse all Create Diagonal Matrices Create a 1-by-5 vector. v = [2 1 -1 -2 -5]; Usediagto create a matrix with the elements ofvon the main diagonal. ...
1Let K be an associative and commutative ring with 1, and k a subring of K such that and the elements 2, 3 are invertible in k. Let n be an integer and an invertible diagonal n by n matrix over k. In the paper, Lie subrings of the general linear Lie ring containing the...
In general, an M-matrix is a real square matrix with nonpositive off-diagonal elements (i.e., a Z-matrix) and whose principal minors are all positive; there are many equivalent characterizations of this class of matrices; see [9, 18]. Problem (1) is the exact formulation of the sparsi...