A skew symmetric matrix is a square matrix in which the elements below the main diagonal are the negatives of the corresponding elements above the main diagonal. In other words, if A is a skew symmetric matrix, then Aij = -Aji for all i and j.
Some key properties of a skew symmetric matrix are that its main diagonal elements are all equal to 0, its transpose is equal to its negative, and its determinant is either 0 (if the matrix is of even order) or a negative number (if the matrix is of odd order).
Skew symmetric matrices are commonly used in linear algebra to represent transformations such as rotations and reflections. They also have applications in mechanics, physics, and computer graphics.
To determine if a matrix is skew symmetric, you can check if it is equal to its negative transpose. Alternatively, you can check if all elements below the main diagonal are the negatives of the corresponding elements above the main diagonal.
No, a skew symmetric matrix must have all its main diagonal elements equal to 0. This is because Aii = -Aii for all i, which is only possible if Aii = 0.