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

 Messages: [ Previous | Next ]
 Dave Rusin Posts: 3,118 Registered: 12/6/04
Re: Failing Linear Algebra:
Posted: Apr 28, 2004 1:23 PM

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

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 Guest
4/22/04 Michael N. Christoff
1/10/07 Gerry Myerson
1/10/07 Jonathan Miller
1/10/07 Guest
1/10/07 David C. Ullrich
1/10/07 Acid Pooh
1/10/07 Guest
4/23/04 Brian Borchers
4/27/04 Guest
1/10/07 maky m.
4/26/04 David Ames
1/10/07 Guest
1/10/07 Michael Stemper
1/10/07 maky m.
4/23/04 Porker899
4/27/04 Guest
1/10/07 Abraham Buckingham
1/10/07 Mitch Harris
1/10/07 Guest
1/10/07 Grey Knight
1/10/07 Guest
1/10/07 Toni Lassila
1/10/07 Thomas Nordhaus
1/10/07 George Cox
4/28/04 Dave Rusin
4/28/04 George Cox
4/28/04 George Cox
4/29/04 Marc Olschok
4/29/04 Mitch Harris
4/29/04 Robert Israel
4/28/04 Guest
4/29/04 Guest
1/10/07 Dave Rusin