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(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 forms, the stiffness matrix will also be symmetric. In other words, ai,j = <φi,φj> = <φj,φi> = ai,j.
The issue is closely related to so-called "Gramian matrices" which, in addition to symmetry, have other properties desirable in the context of FEM. I've provided links below.
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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 a skew symmetric matrix?
A skew symmetric matrix is a square matrix which satisfy, Aij=-Aji or A=-At
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
Why are unrestrained global stiffness matrix singular?
A singular matrix is one that has a determinant of zero, and it has no inverse. Global stiffness can mean rigid motion of the body.
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 a skew symmetric matrix?
A skew symmetric matrix is a square matrix which satisfy, Aij=-Aji or A=-At
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.
What is a symmetric matrix?
a square matrix that is equal to its transpose
Is null square matrix a skew symmetric?
yes, it is both symmetric as well as skew symmetric
What is the definition of a 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 definition of The 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 symbol for skew?
In linear algebra, a skew-symmetric matrix is a square matrix .....'A'
Why are unrestrained global stiffness matrix singular?
A singular matrix is one that has a determinant of zero, and it has no inverse. Global stiffness can mean rigid motion of the body.
What type of matrix is a vector?
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.
