Symmetric matrix: A symmetric matrix is a

Symmetric Matrix A symmetric matrix is a square matrix that is equal to its transpose, meaning its elements are mirrored across the main diagonal. In simple terms, if element aij = aji, the matrix is symmetric . These matrices often arise in mathematics, physics, and data science due to their elegant properties, such as real eigenvalues, orthogonal eigenvectors, and diagonalizability. Symmetric matrices play a key role in simplifying computations and modeling real-world systems efficiently. 1 ... A matrix is called a symmetric matrix if its transpose is equal to the matrix itself. Only a square matrix is symmetric because in linear algebra equal matrices have equal dimensions. How do you know if a matrix is symmetric ? Generally, the symmetric matrix is defined as A = AT Where A is any matrix , and AT is its transpose. If a ij denotes the entries in an i-th row and j-th column, then the symmetric matrix is represented as a ij = a ji Where all the entries of a symmetric matrix are ... 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, (2) where I is the identity matrix . For example, A=[4 1; 1 -2] (3) is a symmetric matrix . Hermitian matrices are a useful generalization of symmetric matrices for complex matrices . A matrix that is not symmetric is said to be an asymmetric matrix , not to be confused with an antisymmetric matrix . A matrix m can be tested to see if...