Let A be the set of all n &#x00D7;<!-- × --> n symmetric real matirix and f

Willow Pratt

Willow Pratt

Answered question

2022-07-12

Let A be the set of all n × n symmetric real matirix and f C ( R , A ). Then whether there is a g C ( R , O ( n ) ) such that for all t R, g ( t ) 1 f ( t ) g ( t ) is a diagonal matrix?

Answer & Explanation

Melina Richard

Melina Richard

Beginner2022-07-13Added 14 answers

No. Consider f ( t ) = ( t 0 0 2 t ) for t 0 and ( 0 t t 0 ) .
For t > 0, g ( t ) must be ( ± 1 0 0 ± 1 ) or ( 0 ± 1 ± 1 0 ) , but for t < 0 all entries of g ( t ) must be ± 1 / 2

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