Page 425 - Advanced Linear Algebra
P. 425
Tensor Products 409
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27. Prove that if and are nonsingular, then so is n ( ) and
²( n )³ c ~ ( c n ) c
28. Prove that tr²( n )³ ~ tr²(³ h tr²)³ .
29. Suppose that is algebraically closed. Prove that if has eigenvalues
(
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ÁÃÁ and ) has eigenvalues ÁÃÁ , both lists including
multiplicity, then ( n ) has eigenvalues ¸ Á ¹ , again
counting multiplicity.
30. Prove that det²( Á n ) Á ³ ~ ² det²( Á ³³ ² det²) Á ³³ .
