Write A Square Matrix Which Is Both Symmetric As Well As Skew Symmetric

11 May, 2021

Suppose A is a matrix then if the transpose of matrix A AT - A. Here 12 A A is the symmetric matrix.

Solved 4 Let A Be A Square Matrix Then A Is Called Symm Chegg Com

So 12 A A A A A.

Write a square matrix which is both symmetric as well as skew symmetric. A is a diagonal matrix B. Every square diagonal matrix is symmetric since all off-diagonal elements are zero. A skew symmetric matrix A T - A.

That is A aij nn is a symmetric matrix then aij a ji for all i and j. A is a zero matrix C. Write a square matrix which is both symmetric as well as skew - symmetric.

And A square matrix is a matrix with the same number of rows and columns. There exists a unique matrix A 0 n n such that it is both symmetric and skew-symmetric. A matrix A with nn dimensions is said to be skew symmetric if and only if aij -aji for all i j such that 1n jn.

Similarly in characteristic different from 2 each diagonal element of a skew-symmetric matrix must be zero since each is its own negative. So B is the correct answer. An n-by-n matrix is known as a square matrix of order n.

A square matrix is symmetric when it is equal to its transpose It is skew symmetric when it is equal to the negation its transpose. A A A A 2A. In linear algebra a real symmetric matrix represents a self-adjoint operator over a real inner product space.

So if its both symmetric and skew symmetric then It follows that so is the zero matrix. A matrix can be skew symmetric only if it is square. If the transpose of a matrix is equal to the negative of itself the matrix is said to be skew symmetric.

If B is a square matrix and A is any square matrix of order equl to that of B prove that B AB is symmetirc or skew symmetric according as A is symmetric or skew symmetric. If B is a square matrix and A is any square matrix of order equl to that of B prove that B AB is symmetirc or skew symmetric according as A is symmetric or skew symmetric. For instance is a symmetric matrix since AT A.

12 A A is the symmetric matrix. If the matrix A is both symmetric and skew-symmetric then A is a a diagonal matrix b zero matrix c square matrix d scalar matrix asked Jan 15 in Matrices by Sadhri. A 0 n n a i j n n 0 i j A a i j n n By the properties of scalar multiplication of matrices.

If the characteristic of the field is 2 then a skew-symmetric matrix is the same thing as a symmetric matrix. Now Lets write matrix A as sum of symmetric skew symmetric matrix. We need to find a square matrix which is both symmetric as.

Observe that transpose of. The elements on the diagonal of a skew-symmetric matrix are zero and therefore its trace equals zero. Since AT - A A is a skew - symmetric matrix.

Thus A 0 0 0 0 is an example of a matrix that is both symmetric and skew - symmetric. A square matrix is said to be skew symmetric if the transpose of the matrix equals its negative. 12 A A 12 A A A.

A is a square matrix D. Any Square matrix can be expressed as sum of a symmetric and Skew symmetric matrix. In other words we can say that matrix A is said to be skew-symmetric if transpose of matrix A is equal to negative of Matrix A ie.

None of these Since A is both symmetric and skew-symmetric matrix A A and A A Comparing both equations A A A A O 2A O A O Therefore A is a zero matrix. The sum of two skew-symmetric matrices is skew-symmetric. It is skew-symmetric matrix because.

This means that for a matrix to be skew symmetric. A square matrix A is said to be symmetric if AT A. Write a square matrix which.

Square Matrix A is said to be skew-symmetric if for all i and j. Lets take an example of matrix. If is either a real or complex matrix then.

We first prove that the object exists. For a given matrix A the symmetric matrix would be half of A plus A tran. A skew-symmetric matrix is a square matrix whose transpose equals its negative that it satisfies the condition.

Note that all the main diagonal elements in skew-symmetric matrix are zero. Symmetric and Skew Symmetric Matrices. Symmetric and Skew Symmetric Matrices.

A scalar multiple of a skew-symmetric matrix is skew-symmetric.

If A Is Skew Symmetric Matrix Of Order 2 And B 1 4 2 9 And C 9 4 2 1 Respectiv Youtube