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What is a symmetric matrix?

In: Algebra, Linear Algebra [Edit categories]

Answer:

a square matrix that is equal to its transpose

First answer by Mathdoc. Last edit by Mathdoc. Contributor trust: 427 [recommend contributor ]. Question popularity: 1 [recommend question].

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Can a zero matrix be a skew symmetric matrix?
My knowledge limits to square matrices. The answer is yes, because 0 = -0
What is a skew symmetric matrix?
A skew symmetric matrix is a square matrix which satisfy, Aij=-Aji or A=-At
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 =- Athat implies 2A =zero matrixthat implies A is a zero matrix
Why is the stiffness matrix symmetric?
(I'm assuming you're referring to FEM) The entries of a stiffness matrix are inner products (bilinear forms) of some basis functions. Insofar as you will typically be dealing with symmetric bilinear...
How to find the Inverse of a square symmetric matrix?
You can factorize the matrix using LU or LDLT factorization algorithm. inverse of a diagonal matrix (D) is really simple. To find the inverse of L, which is a lower triangular matrix, you can find...