What is skew-symmetric matrix explain with an example?

What is skew-symmetric matrix explain with an example?

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 i.e (AT =−A). Note that all the main diagonal elements in the skew-symmetric matrix are zero. Let’s take an example of a matrix. It is skew-symmetric matrix because aij =−aji for all i and j.

Is symmetric and skew-symmetric?

Thus, the zero matrices are the only matrix, which is both symmetric and skew-symmetric matrix.

What is skew matrix class 12?

Class 12 Maths Matrices. Skew Symmetric Matrices. Skew Symmetric Matrices (Square Matrix) A square matrix A = [aij] is said to be skew symmetric matrix if A′ = – A, that is aji = – aij for all possible values of i and j. Now, if we put i = j, we have aii = – aii.

What is symmetric matrix class 12?

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.

What is meant by Skew matrix?

In mathematics, particularly in linear algebra, a skew-symmetric (or antisymmetric or antimetric) matrix is a square matrix whose transpose equals its negative.

Is zero matrix a symmetric matrix?

As we know, a zero matrix is a matrix whose elements are 0. Thus, it satisfies the property of being symmetric. Therefore, the zero matrix is a symmetric matrix.

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.