Show that the product of two 2 times 2 skew symmetric matrices is diagonal. Is this true for n times n skew symmetric matrices with n > 2?

floymdiT 2021-02-03 Answered
Show that the product of two 2×2 skew symmetric matrices is diagonal. Is this true for n×n skew symmetric matrices with n > 2?
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Expert Answer

Theodore Schwartz
Answered 2021-02-04 Author has 99 answers
Step 1
Given:
Show that the product of two 2×2 skew symmetric matrices is diagonal. Is this true for n×n skew symmetric
matrices with n > 2?
Step 2
Explanation:
Since skew−symmetric matrix is of the form given below aij=aji
Consider skew−symmetric matrix A and B,
A=[0aa0],B=[0bb0]
AB=[0aa0][0bb0]=[ab00ab]
Since product of 2×2 skew−symmetric matrix is diagonal.Since this is only true for n×n skew−symmetric matrices.where , n=2
Hence the solution.
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Jeffrey Jordon
Answered 2022-01-24 Author has 2064 answers
Jeffrey Jordon
Answered 2022-01-27 Author has 2064 answers

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