HI,

How can I prove the set of compact matrices are compact

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- Apr 27th 2005, 11:29 AMakscolaOrthognal matrices are compact
HI,

How can I prove the set of compact matrices are compact - Apr 27th 2005, 12:21 PMMath Help
Do you mean Orthogonal matrices are compact You wrote:

How can I prove the set of**compact**matrices are compact - Apr 28th 2005, 03:33 AMakscolaOrthognal matrices are compact
Yes.Set of orthogonal matrices are compact.I now why they are bounded but does not know why they are closed.

- Apr 29th 2005, 08:30 AMShmuel
Please give us an equation to define the matrix.

- Apr 29th 2005, 09:28 AMhpeQuote:

Originally Posted by**Math Help**

The condition A'A = E actually is a set of n^2 equations that have to hold. The left hand side of each equation is a continuous function on the set of all nxn matrices (just a quadratic form, actually). The right hand side of each equation is either 0 or 1, a closed set.

Preimages of closed sets under continuous functions are closed.

Finite intersections of closed sets are closed.

Done: O is closed. (You already proved it's bounded). - May 23rd 2009, 03:27 PMdeannalouise
Can you explain how you know they are bounded? Thanks.

- May 24th 2009, 04:50 PMhpe