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How that a matrix which is both symmetric and skew symmetric is a zero matrix?
Let A = [aij] be a matrix which is both symmetric and skew symmetric. Since A is a skew symmetric matrix, so A′ = –A. Again, since A is a symmetric matrix, so A′ = A. Hence A is a zero matrix.
How do you check if a matrix is symmetric or skew symmetric?
Skew-Symmetric Matrix
- A square matrix, A , is skew-symmetric if it is equal to the negation of its nonconjugate transpose, A = -A. ‘ .
- Since real matrices are unaffected by complex conjugation, a real matrix that is skew-symmetric is also skew-Hermitian. For example, the matrix.
Is matrix a symmetric or skew symmetric give a reason?
A square matrix which is equal to its transpose is known as a symmetric matrix. Only square matrices are symmetric because only equal matrices have equal dimensions….Conditions for Symmetric and Skew Symmetric Matrix.
| SYMMETRIC MATRIX(A) | AT=A aji=(aij) |
|---|---|
| SKEW SYMMETRIC MATRIX (A) | AT=(-A) aji=(-aij) |
Is symmetric and skew both?
Thus, the zero matrices are the only matrix, which is both symmetric and skew-symmetric matrix. Hence, option B is correct.
Can skew-symmetric matrix be zero matrix?
The zero matrix has that property, so it is a skew-symmetric matrix. Skew-symmetric matrices also form a vector space, and the zero matrix is the zero vector. In fact, the zero matrix is only matrix which is both symmetric and skew-symmetric.
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 difference between symmetric and skew-symmetric matrix?
A symmetric matrix and skew-symmetric matrix both are square matrices. But the difference between them is, the symmetric matrix is equal to its transpose whereas skew-symmetric matrix is a matrix whose transpose is equal to its negative.
What is difference between symmetric and skew symmetric matrix?
A matrix is symmetric if and only if it is equal to its transpose. All entries above the main diagonal of a symmetric matrix are reflected into equal entries below the diagonal. A matrix is skew-symmetric if and only if it is the opposite of its transpose.
Is a zero matrix A skew-symmetric matrix?
Is both symmetric and skew matrix then A is?
(A) A is a diagonal matrix.
What type of a matrix is a if A is both symmetric and skew symmetric?
Does a symmetric matrix be always square matrix?
A symmetric matrix will hence always be square . Some examples of symmetric matrices are: Addition and difference of two symmetric matrices results in symmetric matrix. If A and B are two symmetric matrices and they follow the commutative property, i.e. AB =BA, then the product of A and B is symmetric.
Is every positive definite matrix symmetric?
A Hermitian (or symmetric) matrix is positive definite iff all its eigenvalues are positive. Therefore, a general complex (respectively, real) matrix is positive definite iff its Hermitian (or symmetric) part has all positive eigenvalues.
What is the definition of a symmetric matrix?
In linear algebra, a symmetric matrix is a square matrix that is equal to its transpose. Formally, matrix A is symmetric if.
What is an example of symmetric property?
Geometry – Symmetry. Describe a real world example of the symmetric property. Examples could be: Helical Symmetry. Reflective Symmetry. Rotational Symmetry. Translational Symmetry.