- #1
bernoli123
- 11
- 0
how can we prove that the rank of skew symmetric matrix is even
i could prove it by induction
is there another way
i could prove it by induction
is there another way
A skew symmetric matrix is a square matrix in which the elements satisfy the property that the element at the ith row and jth column is equal to the negative of the element at the jth row and ith column. In other words, the matrix is symmetric about its main diagonal, with all elements on the main diagonal being equal to 0.
A symmetric matrix is a square matrix in which the elements are equal to their corresponding elements when reflected along the main diagonal. In contrast, a skew symmetric matrix is also symmetric, but with the additional property that the elements on the main diagonal are equal to 0 and the elements below the main diagonal are equal to the negative of the elements above the main diagonal.
Skew symmetric matrices are commonly used in mathematical and scientific fields, such as physics and engineering, to represent physical quantities and equations. They are also used in computer graphics and computer vision to represent rotations and reflections in 3D space.
A matrix can be determined to be skew symmetric by checking if its transpose is equal to its negative. In other words, if A is a skew symmetric matrix, then AT = -A. Additionally, the main diagonal of a skew symmetric matrix will be filled with 0s, and the elements above the main diagonal will be equal to the negative of the elements below the main diagonal.
No, a non-square matrix cannot be skew symmetric. The definition of a skew symmetric matrix requires it to be a square matrix with equal number of rows and columns. A non-square matrix cannot satisfy the property of having equal elements on the main diagonal and being symmetric about the main diagonal.