What is a dimension of a symmetric matrix?
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We tackle the case of skew-symmetric first, which yields the condition that for any matrix with real entries, a i j = − a i j , so this means one side of the matrix is completely determined by the other as shown. degree of freedom and that is the dimension we seek
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A square matrix A is said to be symmetric if aij = aji for all i and j, where aij is an element present at (i,j)th position (ith row and jth column in matrix A) and aji is an element present at (j,i)th position (jth row and ith column in matrix A). In other words, we can say that matrix A is said to be symmetric if the transpose of matrix A is equal to matrix A itself (A^T=A).
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