For a matrix M = {m_{ij}}, i,j = 1,2,3,4, the diagonal elements are all zero and m_{ij} = -m_{ji}. The minimum number of...

Question

For a matrix M = {m_{ij}}, i,j = 1,2,3,4, the diagonal elements are all zero and m_{ij} = -m_{ji}. The minimum number of elements required to fully specify the matrix is ______

A. 6
B. 6
C. 12
D. 16

Accepted Answer

The minimum number of elements required to fully specify the matrix is 6. We have a 4x4 matrix where all diagonal entries are zero and m_{ij} = -m_{ji} (skew-symmetric). Since the diagonal is fixed at zero and each off-diagonal entry determines its mirror, we only need to specify the upper triangular (or lower triangular) entries. For a 4x4 matrix, the number of upper-triangular off-diagonal entries is C(4,2) = 6.

For a matrix M = {m_{ij}}, i,j = 1,2,3,4, the diagonal elements are all zero and m_{ij} = -m_{ji}. The minimum number of elements required to fully specify the matrix is ______ A. 6 B. 6 C. 12 D. 16