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

Willow Pratt 2022-07-12 Answered
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?
You can still ask an expert for help

Want to know more about Matrix transformations?

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Answers (1)

Melina Richard
Answered 2022-07-13 Author has 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
Not exactly what you’re looking for?
Ask My Question

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

New questions