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Topic: Failing Linear Algebra:
Replies: 54   Last Post: Jan 10, 2007 12:47 PM

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Dave Rusin

Posts: 3,118
Registered: 12/6/04
Re: Failing Linear Algebra:
Posted: Apr 28, 2004 1:23 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

In article <c98b1ba0.0404271113.66efce63@posting.google.com>,
Anonymous wrote:

>I already bought the text, the Cliff's
>Notes guide to linear algebra, a 2003-version of the Schaum's outline,
>and I even have an old 1968 version of Schaum's that my grandmother
>used when she majored in math.


This is not your grandmother's Linear Algebra course!
(I've always wanted to say something like that.)

>Maybe, if it isn't too much to ask, would anyone here be willing to
>post some problems relating to mappings/kernel/image/isomorphims
>and/or eigenvalues/eigenvectors, and I can attempt to solve them with
>your help?


Sample question
(a) Prove that the set M of all n by n matrices is a vector space (using
familiar matrix addition and scalar multiplication.) What is its
dimension?
(b) Prove that the map f(x) = x^t is a linear transformation from M to M
What is its kernel?
(c) Compute the eigenvalues of f and find the eigenspaces.

I am of course deliberately choosing a question which emphasizes the
proper use of terminology and abstraction, but this is a perfectly
reasonable exam question. (IMHO -- but I have a reputation for thinking
"interesting" questions are reasonable so maybe you shouldn't trust me.)

dave


Date Subject Author
4/22/04
Read Failing Linear Algebra:
Guest
4/22/04
Read Re: Failing Linear Algebra:
Michael N. Christoff
1/10/07
Read Re: Failing Linear Algebra:
Gerry Myerson
1/10/07
Read Re: Failing Linear Algebra:
Jonathan Miller
1/10/07
Read Re: Failing Linear Algebra:
Guest
1/10/07
Read Re: Failing Linear Algebra:
David C. Ullrich
1/10/07
Read Re: Failing Linear Algebra:
Acid Pooh
1/10/07
Read Re: Failing Linear Algebra:
Guest
4/23/04
Read Re: Failing Linear Algebra:
Russell Blackadar
4/23/04
Read Re: Failing Linear Algebra:
Brian Borchers
4/27/04
Read Re: Failing Linear Algebra:
Guest
1/10/07
Read Re: Failing Linear Algebra:
maky m.
4/26/04
Read Re: Failing Linear Algebra:
David Ames
1/10/07
Read Re: Failing Linear Algebra:
Guest
1/10/07
Read Re: Failing Linear Algebra:
Michael Stemper
1/10/07
Read Re: Failing Linear Algebra:
maky m.
4/23/04
Read Re: Failing Linear Algebra:
Porker899
4/27/04
Read Re: Failing Linear Algebra:
Guest
1/10/07
Read Re: Failing Linear Algebra:
Abraham Buckingham
1/10/07
Read Re: Failing Linear Algebra:
Mitch Harris
1/10/07
Read Re: Failing Linear Algebra:
Guest
1/10/07
Read Re: Failing Linear Algebra:
Grey Knight
1/10/07
Read Re: Failing Linear Algebra:
Guest
1/10/07
Read Re: Failing Linear Algebra:
Toni Lassila
1/10/07
Read Re: Failing Linear Algebra:
Thomas Nordhaus
1/10/07
Read Re: Failing Linear Algebra:
George Cox
4/28/04
Read Re: Failing Linear Algebra:
Dave Rusin
4/28/04
Read Re: Failing Linear Algebra:
George Cox
4/28/04
Read Re: Failing Linear Algebra:
George Cox
4/29/04
Read Re: Failing Linear Algebra:
Marc Olschok
4/29/04
Read Re: Failing Linear Algebra:
Mitch Harris
4/29/04
Read Re: Failing Linear Algebra:
Robert Israel
1/10/07
Read Re: Failing Linear Algebra:
Russell Blackadar
4/28/04
Read Re: Failing Linear Algebra:
Guest
1/10/07
Read Re: Failing Linear Algebra:
Russell Blackadar
4/29/04
Read Re: Failing Linear Algebra:
Russell Blackadar
4/29/04
Read Re: Failing Linear Algebra:
Guest
1/10/07
Read Re: Failing Linear Algebra:
Russell Blackadar
1/10/07
Read Re: Failing Linear Algebra:
Russell Blackadar
5/1/04
Read Re: Failing Linear Algebra:
Russell Blackadar
1/10/07
Read Re: Failing Linear Algebra:
Russell Blackadar
1/10/07
Read Re: Failing Linear Algebra:
Dave Rusin
1/10/07
Read Re: Failing Linear Algebra:
Russell Blackadar
4/30/04
Read Re: Failing Linear Algebra:
Guest
1/10/07
Read Re: Failing Linear Algebra:
Guest
1/10/07
Read Re: Failing Linear Algebra:
David C. Ullrich
4/27/04
Read Re: Failing Linear Algebra:
Guest
4/27/04
Read Re: Failing Linear Algebra:
Guest
4/28/04
Read Re: Failing Linear Algebra:
Guest
1/10/07
Read Re: Failing Linear Algebra:
Law Hiu Chung
4/30/04
Read Re: Failing Linear Algebra:
Guest
1/10/07
Read Re: Failing Linear Algebra:
David C. Ullrich

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