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In linear algebra, a symmetric matrix is a square matrix that is equal to its transpose. Formally, Symmetry of a 5×5 matrix Skew-symmetric · Persymmetric matrix · Centrosymmetric matrix
Симметричная матрица Симметричная матрица
Симметричной называют квадратную матрицу, элементы которой симметричны относительно главной диагонали. Более формально, симметричной называют такую матрицу A, что \forall i, j:a_{{ij}}=a_{{ji}}. Это означает, что она равна её транспонированной... Википедия
A symmetric matrix is defined as a square matrix that is equal to its transpose. A symmetric matrix can A can therefore satisfies the condition, A = A^T.
A symmetric matrix is a matrix that is symmetric along the diagonal, which means Aᵀ = A , or in other words, the matrix is equal to its transpose.
A symmetric matrix is a square matrix that satisfies A^(T)=A, (1) where A^(T) denotes the transpose, so a_(ij)=a_(ji). This also implies A^(-1)A^(T)=I, ...
25 июл. 2019 г. · 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.
30 апр. 2024 г. · Symmetric and Skew Symmetric Matrices are the types of square matrices based on the relation between a matrix and its transpose.
Theorem 1: For any square matrix A with real number entries, A + A′ is a symmetric matrix and A – A′ is a skew-symmetric matrix.
A matrix that does not change when the transpose is taken, i.e., A = A T , is called a symmetric matrix. The main diagonal of a matrix is defined as the all ...
crucial properties: ▷ All eigenvalues of a real symmetric matrix are real. ▷ Eigenvectors corresponding to distinct eigenvalues are orthogonal.
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