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Prove that a matrix which is both symmetric as well as skew symmetric is a null matrix?
Let A be a matrix which is both symmetric and skew symmetric. so AT=A and AT= -A so A =- A that implies 2A =zero matrix that implies A is a zero matrix
What is the eigen value of a real symmetric matrix?
The eigen values of a real symmetric matrix are all real.
What is a symmetric matrix?
a square matrix that is equal to its transpose
What is the definition of a skew-Hermitian matrix?
Skew-Hermitian matrix defined:If the conjugate transpose, A†, of a square matrix, A, is equal to its negative, -A, then A is a skew-Hermitian matrix.Notes:1. The main diagonal elements of a skew-Hermitian matrix must be purely imaginary, including zero.2. The cross elements of a skew-Hermitian matrix are complex numbers having equal imaginary part values, and equal-in-magnitude-but-opposite-in-sign real parts.
What is the definition of an anti-symmetric matrix?
The Definition of an Anti-Symmetric Matrix:If a square matrix, A, is equal to its negative transpose, -A', then A is an anti-symmetric matrix.Notes:1. All diagonal elements of A must be zero.2. The cross elements of A must have the same magnitude, but opposite sign.
Prove that a matrix which is both symmetric as well as skew symmetric is a null matrix?
Let A be a matrix which is both symmetric and skew symmetric. so AT=A and AT= -A so A =- A that implies 2A =zero matrix that implies A is a zero matrix
Is null square matrix a skew symmetric?
yes, it is both symmetric as well as skew symmetric
What is the symbol for skew?
In linear algebra, a skew-symmetric matrix is a square matrix .....'A'
Under what condition is the product of skew-symmetric matrices skew-symmetric?
I could be wrong but I do not believe that it is possible other than for the null matrix.
Can a zero matrix be a skew symmetric matrix?
My knowledge limits to square matrices. The answer is yes, because 0 = -0
What is the dimension of a skew symmetric matrix of order 3?
In a skew symmetric matrix of nxn we have n(n-1)/2 arbitrary elements. Number of arbitrary element is equal to the dimension. For proof, use the standard basis.Thus, the answer is 3x2/2=3 .
Are the property of symmetric and skew symmetric are invariant?
yes
C programme for symmetric and skew symmetric matrices?
#include<iostream.h>
Are skew symmetric roots purely real or purely imaginary?
They can be either. If they are roots of a real polynomial then purely imaginary would be symmetric and only real roots can be skew symmetric.
When you call adjacency matrix in symmetric matrix?
If your graph is undirected, then its adjacency matrix will be symmetric. Faizan
What is the definition of a symmetric matrix?
Symmetric Matrix:Given a square matrix A such that A'=A, where A' is the transpose of A, then A is a symmetric matrix.note: No need to think about diagonal elements, they can be anything.
What is the eigen value of a real symmetric matrix?
The eigen values of a real symmetric matrix are all real.
