The main diagonal entries are zero because implies .
The matrix is skew-symmetric if and only if , where is the matrix transpose
For the trace operator, we have that . Combining this with property (1), it follows that for a skew-symmetric matrix .
Skew-symmetric matrices form a vector space: If and are skew-symmetric and , then is also skew-symmetric.
Suppose is a skew-symmetric matrix and is a matrix of same order as . Then is skew-symmetric.
According to Jacobi’s Theorem, the determinant of a skew-symmetric matrix of odd order is zero.
|Date of creation||2013-03-22 12:01:05|
|Last modified on||2013-03-22 12:01:05|
|Last modified by||Daume (40)|