Q: What is the definition of a symmetric matrix?

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If your graph is undirected, then its adjacency matrix will be symmetric. Faizan

yes, it is both symmetric as well as skew symmetric

In linear algebra, a skew-symmetric matrix is a square matrix .....'A'

My knowledge limits to square matrices. The answer is yes, because 0 = -0

I could be wrong but I do not believe that it is possible other than for the null matrix.

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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.

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.

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.

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

A skew symmetric matrix is a square matrix which satisfy, Aij=-Aji or A=-At

If your graph is undirected, then its adjacency matrix will be symmetric. Faizan

The eigen values of a real symmetric matrix are all real.

a square matrix that is equal to its transpose

yes, it is both symmetric as well as skew symmetric

In linear algebra, a skew-symmetric matrix is a square matrix .....'A'

Vector matrix has both size and direction. There are different types of matrix namely the scalar matrix, the symmetric matrix, the square matrix and the column matrix.

To determine if an array is symmetric, the array must be square. If so, check each element against its transpose. If all elements are equal, the array is symmetric.For a two-dimensional array (a matrix) of order n, the following code will determine if it is symmetric or not:templatebool symmetric(const std::array& matrix){for (size_t r=0 ; r