What is the difference between symmetric and skew-symmetric matrices?
Answer (1)
A square matrix A is said to be symmetric if a ij = a j i for all i and j, where a ij is an element present at (i,j) th position (i th row and j t h column in matrix A) and a ji is an element present at (j,i) th position (j th row and i th column in matrix A) whereas square matrix A is said to be skew-symmetric if a ij =−a ji for all i and j. In other words, we can say that matrix A is said to be skew-symmetric if the transpose of matrix A is equal to the negative of matrix A i.e (A T =−A)
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