About discrete structure in CS class, a square matrix of dimension n is called a diagonal...
About discrete structure in CS class, a square matrix of dimension
n is called a diagonal matrix if all cells except the left diagonal
(cell positions (1, 1), (2, 2), (3, 3), …) contain 0. Suggest a
quicker method (different from the standard method) to find the
product of two diagonal matrices of size n.
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About discrete structure in CS class, a square matrix of dimension
n is called a diagonal...
A square matrix is called skew-symmetric if AT = -A. (a) (4 points) Explain why the...
A square matrix is called skew-symmetric if AT = -A. (a) (4 points) Explain why the main diagonal of a skew-symmetric matrix consists entirely of zeros. (b) (2 points) Provide examples of a 2 x 2 skew-symmetric matrix and a 3 x 3 skew-symmetric matrix. (6 points) Prove that if A and B are both n x n skew-symmetric matrices and c is a nonzero scalar, then A + B and cA are both skew-symmetric as well. (4 points) Find...
*** Write a function called reverse_diag that creates a square matrix whose elements are 0 except...
*** Write a function called reverse_diag that creates a square matrix whose elements are 0 except for 1s on the reverse diagonal from top right to bottom left. The reverse diagonal of an nby- n matrix consists of the elements at the following indexes: (1, n), (2, n-1), (3, n-2), … (n, 1). The function takes one positive integer input argument named n, which is the size of the matrix, and returns the matrix itself as an output argument. Note...
3. A Latin square of order n with entries in Z is called idempotent if the entries on the main diagonal from upper...
3. A Latin square of order n with entries in Z is called idempotent if the entries on the main diagonal from upper left to lower right are 0, 1, 2, . . . , n-1 in that order. (a) Prove that any symmetric idempotent Latin square must have odd order (b) Let n -2m +1 for a positive integer m. Construct the nx n array A whose i,j entry is given by (m +1) (i+j (mod Prove that this...
(1 point) The trace of a square n x n matrix A = (aii) is the...
(1 point) The trace of a square n x n matrix A = (aii) is the sum ani + 022 + ... + ann of the entries on its main diagonal. Let V be the vector space of all 2 x 2 matrices with real entries. Let H be the set of all 2 x 2 matrices with real entries that have trace 1. Is Ha subspace of the vector space V? 1. Does H contain the zero vector of...
An Triangular matrix is a square matrix whose elements below the diagonal are defined to be...
An Triangular matrix is a square matrix whose elements below the diagonal are defined to be 0. For example, the matrix element Mr,c = 0 if r > c. The following is an example matrix of size 4. 0 1 2 3 0 100 200 300 400 1 0 500 600 700 2 0 0 800 900 3 0 0 0 1000 While it is possible to use a regular 2D array to represent an Triangular matrix, doing so is...
Question A matrix of dimensions m × n (an m-by-n matrix) is an ordered collection of m × n elemen...
Question A matrix of dimensions m × n (an m-by-n matrix) is an ordered collection of m × n elements. which are called eernents (or components). The elements of an (m × n)-dimensional matrix A are denoted as a,, where 1im and1 S, symbolically, written as, A-a(1,1) S (i.j) S(m, ). Written in the familiar notation: 01,1 am Gm,n A3×3matrix The horizontal and vertical lines of entries in a matrix are called rows and columns, respectively A matrix with the...
C++ CODE: The matrix class consists of two files: matrix.h and matrix.cpp. The class has the...
C++ CODE: The matrix class consists of two files: matrix.h and matrix.cpp. The class has the following definition: matrix -size:int -mat:int** ---------------- +matrix(file:string) +~matrix() +operator +(add:matrix*):matrix & +operator-(sub:matrix*):matrix & +friend operator<<(out:ostream &, t:const matrix&):ostream & +displayRow(r:int):void The class variables are as follows: • size: the number of rows and columns in a square matrix • mat: the integer matrix that contains the numeric matrix itself. The methods have the following behaviour: 2 • matrix(file:string): The default constructor. It receives the...
Theory: A vector with nonnegative entries is called a probability vector if the sum of its entries is 1. A square matrix...
Theory: A vector with nonnegative entries is called a probability vector if the sum of its entries is 1. A square matrix is called right stochastic matrix if its rows are probability vectors; a square matrix is called a left stochastic matrix if its columns are probability vectors; and a square matrix is called a doubly stochastic matrix if both the rows and the columns are probability vectors. **Write a MATLAB function function [S1,S2,P]=stochastic(A) which accepts a square matrix A...
Using MATLAB, develop an M-file to determine LU factorization of a square matrix with partial pivoting....
Using MATLAB, develop an M-file to determine LU factorization of
a square matrix with partial pivoting. That is, develop a function
called mylu that is passed the square matrix [A] and returns the
triangular matrices [L] and [U] and the permutation P. You are not
to use MATLAB built-in function lu in your codes. Test your
function by using it to solve a system of equations listed below in
part 3. Confirm that your function is working properly by verifying...
(f) Let A be symmetric square matrix of order n. Show that there exists an orthogonal matrix P su...
(f) Let A be symmetric square matrix of order n. Show that there exists an orthogonal matrix P such that PT AP is a diagonal matrix Hint : UseLO and Problem EK〗 (g) Let A be a square matrix and Rn × Rn → Rn is defined by: UCTION E AND MES FOR THE la(x, y) = хтАУ (i) Show that I is symmetric, ie, 14(x,y) = 1a(y, x), if a d Only if. A is symmetric (ii) Show that...
A square matrix is called skew-symmetric if AT = -A. (a) (4 points) Explain why the main diagonal of a skew-symmetric matrix consists entirely of zeros. (b) (2 points) Provide examples of a 2 x 2 skew-symmetric matrix and a 3 x 3 skew-symmetric matrix. (6 points) Prove that if A and B are both n x n skew-symmetric matrices and c is a nonzero scalar, then A + B and cA are both skew-symmetric as well. (4 points) Find...
3. A Latin square of order n with entries in Z is called idempotent if the entries on the main diagonal from upper left to lower right are 0, 1, 2, . . . , n-1 in that order. (a) Prove that any symmetric idempotent Latin square must have odd order (b) Let n -2m +1 for a positive integer m. Construct the nx n array A whose i,j entry is given by (m +1) (i+j (mod Prove that this...
(1 point) The trace of a square n x n matrix A = (aii) is the sum ani + 022 + ... + ann of the entries on its main diagonal. Let V be the vector space of all 2 x 2 matrices with real entries. Let H be the set of all 2 x 2 matrices with real entries that have trace 1. Is Ha subspace of the vector space V? 1. Does H contain the zero vector of...
Question A matrix of dimensions m × n (an m-by-n matrix) is an ordered collection of m × n elements. which are called eernents (or components). The elements of an (m × n)-dimensional matrix A are denoted as a,, where 1im and1 S, symbolically, written as, A-a(1,1) S (i.j) S(m, ). Written in the familiar notation: 01,1 am Gm,n A3×3matrix The horizontal and vertical lines of entries in a matrix are called rows and columns, respectively A matrix with the...
Using MATLAB, develop an M-file to determine LU factorization of
a square matrix with partial pivoting. That is, develop a function
called mylu that is passed the square matrix [A] and returns the
triangular matrices [L] and [U] and the permutation P. You are not
to use MATLAB built-in function lu in your codes. Test your
function by using it to solve a system of equations listed below in
part 3. Confirm that your function is working properly by verifying...
(f) Let A be symmetric square matrix of order n. Show that there exists an orthogonal matrix P such that PT AP is a diagonal matrix Hint : UseLO and Problem EK〗 (g) Let A be a square matrix and Rn × Rn → Rn is defined by: UCTION E AND MES FOR THE la(x, y) = хтАУ (i) Show that I is symmetric, ie, 14(x,y) = 1a(y, x), if a d Only if. A is symmetric (ii) Show that...
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