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Symmetric, Anti- symmetric, Orthogonal Matrices Video Lecture | Mathematical Methods - Physics
FAQs on Symmetric, Anti- symmetric, Orthogonal Matrices Video Lecture - Mathematical Methods - Physics
| 1. What is a symmetric matrix? |  |
Ans. A symmetric matrix is a square matrix that is equal to its transpose. In other words, the elements of a symmetric matrix are symmetric with respect to the main diagonal.
| 2. What is an anti-symmetric matrix? | |
Ans. An anti-symmetric matrix is a square matrix that is equal to the negative of its transpose. In other words, the elements of an anti-symmetric matrix satisfy the condition A^T = -A.
| 3. What is an orthogonal matrix? | |
Ans. An orthogonal matrix is a square matrix where the transpose of the matrix is equal to its inverse. This means that for an orthogonal matrix A, A^T * A = I, where I is the identity matrix.
| 4. How can symmetric matrices be identified? | |
Ans. Symmetric matrices can be identified by checking if the matrix is equal to its transpose. If A = A^T, then the matrix is symmetric.
| 5. Can a matrix be both symmetric and orthogonal at the same time? | |
Ans. Yes, a matrix can be both symmetric and orthogonal if it satisfies the conditions of being equal to its transpose and having its transpose be equal to its inverse.
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