Table of Contents
- 1 What is the inverse of a skew symmetric matrix of even order?
- 2 Is skew symmetric matrix of even order is always singular?
- 3 What is the inverse of a skew symmetric matrix of odd order?
- 4 What is the inverse of symmetric matrix?
- 5 Which matrix is both symmetric and skew symmetric matrix?
- 6 What is the determinant of skew-symmetric matrix of odd order?
- 7 What is the inverse of a diagonal matrix?
What is the inverse of a skew symmetric matrix of even order?
But from (1) we see that (-A)(-B)=(-B)(-A) = I, showing that -B is the inverse matrix of -A. From (1) and (2), by uniqueness of inverse of -A, we see that B’ = -B. Hence we see that the inverse matrix of a skew-symmetrix of even order is also skew-symmetric.
Is skew symmetric matrix of even order is always singular?
Hence, all odd dimension skew symmetric matrices are singular as their determinants are always zero. This result is called Jacobi’s theorem, after Carl Gustav Jacobi (Eves, 1980). . Thus the determinant of a real skew-symmetric matrix is always non-negative.
What is the determinant of a skew symmetric matrix of even order?
Det of a skew symmetric matrix of even order is a non-zero perfect square.
What is the inverse of a skew symmetric matrix of odd order?
(A−1)T=(AT)−1, where A is a non-singular symmetric matrix.
What is the inverse of symmetric matrix?
Therefore, the inverse of a symmetric matrix is a symmetric matrix. Thus, the correct option is A. a symmetric matrix. Note: A symmetric matrix is a square matrix that is equal to its transpose.
What is the sum of symmetric and skew symmetric matrix?
Any Square matrix can be expressed as the sum of a symmetric and a skew-symmetric matrix. Proof: Let A be a square matrix then, we can write A = 1/2 (A + A′) + 1/2 (A − A′). From the Theorem 1, we know that (A + A′) is a symmetric matrix and (A – A′) is a skew-symmetric matrix.
Which matrix is both symmetric and skew symmetric matrix?
zero matrices
Thus, the zero matrices are the only matrix, which is both symmetric and skew-symmetric matrix.
What is the determinant of skew-symmetric matrix of odd order?
Skew Symmetric determinant of odd order is zero.
What is an odd order skew-symmetric matrix?
A. Zero. B. Hint: A matrix is skew- symmetric if and if it is the opposite of its transpose and the general properties of determinants is given as det(A)=det(AT) and det(−A)=(−1)ndet(A) where n is number of rows or columns of square matrix. …
What is the inverse of a diagonal matrix?
The inverse of a diagonal matrix is obtained by replacing each element in the diagonal with its reciprocal, as illustrated below for matrix C. where I is the identity matrix. This approach will work for any diagonal matrix, as long as none of the diagonal elements is equal to zero.