What is the minimum rank of a skew symmetric matrix?

[bhanesh]

What is minimum possible rank of skew symmetric matrix ?

 

[jgens]

Look at the zero matrix.

 

[bhanesh]

But how can we say that zero matrix is skew symmetric matrix

 

[jgens]

If 0 denotes the zero matrix, then 0^T + 0 = 0. So this matrix is skew-symmetric.

 

[mathwonk]

a little more surprising question might be what is the maximum rank, say of a 3by3 skew symmetric matrix?

 

[bhanesh]

Determinant of skew symmetric matrix of odd order is always zero. So for skew symmetric matrix its rank will be always even in number. ..