What is the minimum rank of a skew symmetric matrix?

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The minimum rank of a skew symmetric matrix is zero, as the zero matrix qualifies as skew symmetric. A skew symmetric matrix is defined by the property that its transpose equals its negative. For a 3x3 skew symmetric matrix, the maximum rank is 2, since the determinant of any skew symmetric matrix of odd order is always zero. Consequently, the rank of skew symmetric matrices is always an even number. Understanding these properties is crucial for studying the characteristics of skew symmetric matrices.
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What is minimum possible rank of skew symmetric matrix ?
 
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Look at the zero matrix.
 
But how can we say that zero matrix is skew symmetric matrix
 
If 0 denotes the zero matrix, then 0T + 0 = 0. So this matrix is skew-symmetric.
 
a little more surprising question might be what is the maximum rank, say of a 3by3 skew symmetric matrix?
 
Determinant of skew symmetric matrix of odd order is always zero. So for skew symmetric matrix its rank will be always even in number. ..
 

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