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Tag Archives: Linear Algebra
Consider the real numbers for . Prove that
Using the identity in combination with we have:
Let such that
Prove that if is odd.
Let be unitary linearly independent vectors. Evaluate the determinant
where denotes the outer product.
Let and such that . Prove that
Since is real, its complex eigenvalues come in conjugate pairs. Thus, in this case we conclude that has eigenvalues .
Now, if is an eigenvalue of , then is an eigenvalue of . Thus, the matrix has eigenvalues and .
Now, is the product of these eigenvalues, which is to say
Let . Prove that .
The characteristic polynomial of is . This in return means and . Thus,