Talk:Linear algebra

We should cover:

High school topics:

• Matrix representation of linear equations
• Resolution: Gauss and Crammer. Determinants.
• Matrix multiplication.
• Matrix basic operations (addition, traspose, ...)

High school / University ?:

• Bilinear forms
• Quadratic forms

University topics:

• Properties of a linear system
• Vector spaces and subspaces
• Matrix inversion
• Bases. Orthogonal and orthonormal bases.
• Elementary matrices
• Similarity transformations
• Gram-Schmidt orthonormalization
• ...?
• Diagonalization
  • ...
  • ...
  • Finding orthogonal and orthonormal bases
  • Diagonalization of bilinear/quadratic forms
    • Positive-definite, negative-definite, semidefinite and indefinite matrices. Scalar product
  • Matrix exponentiation by diagonalizing
• Jordan canonical form
• Factorization methods
  • LU factorization
  • Cholesky
  • Singular value decomposition
• Applications
  • Matrix differential equations
  • Least squares fitting
  • Principle components analysis

Feel free to edit the list. It isn't complete at all, but I'm tired... --Jorge 18:51, 12 April 2007 (UTC)

I added some :-) --HappyCamper 15:21, 13 April 2007 (UTC)

They thaught you quadratic forms in high school? Wow. Where are you from? --Jorge 22:50, 30 April 2007 (UTC)

Teachers make all the difference :-) Anyway, should we keep on adding more items to this list? Or just start collecting materials? --HappyCamper 05:42, 2 May 2007 (UTC)

In general, I think we should avoid duplicating information already available on wikipedia. We can just add the links to this information, instead. What we can do though, is add some good exercises/examples. This is stuff that shouldn't be on wikipedia, but should be on wikiversity. I think I'll begin working on the discussion of eigenvalues and eigenvectors, since it is such a powerful concept in mathematics.132.235.38.246 13:11, 28 April 2009 (UTC)