What does symmetric matrix mean?
Definitions for symmetric matrix
sym·met·ric ma·trix
This dictionary definitions page includes all the possible meanings, example usage and translations of the word symmetric matrix.
Wiktionary
symmetric matrixnoun
A square matrix that is its own transpose, and is symmetric about the main diagonal
Wikidata
Symmetric matrix
In linear algebra, a symmetric matrix is a square matrix that is equal to its transpose. Let A be a symmetric matrix. Then: The entries of a symmetric matrix are symmetric with respect to the main diagonal. So if the entries are written as A =, then aij = aji, for all indices i and j. The following 3×3 matrix is symmetric: Every diagonal matrix is symmetric, since all off-diagonal entries are zero. Similarly, each diagonal element of a skew-symmetric matrix must be zero, since each is its own negative. In linear algebra, a real symmetric matrix represents a self-adjoint operator over a real inner product space. The corresponding object for a complex inner product space is a Hermitian matrix with complex-valued entries, which is equal to its conjugate transpose. Therefore, in linear algebra over the complex numbers, it is often assumed that a symmetric matrix refers to one which has real-valued entries. Symmetric matrices appear naturally in a variety of applications, and typical numerical linear algebra software makes special accommodations for them.
Numerology
Chaldean Numerology
The numerical value of symmetric matrix in Chaldean Numerology is: 8
Pythagorean Numerology
The numerical value of symmetric matrix in Pythagorean Numerology is: 3
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"symmetric matrix." Definitions.net. STANDS4 LLC, 2024. Web. 29 Apr. 2024. <https://www.definitions.net/definition/symmetric+matrix>.
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