Difference between revisions of "Linear algebra"
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*[[Linear equations]] | *[[Linear equations]] | ||
:*coefficient matrices and Gauss-Jordan elimination | :*coefficient matrices and Gauss-Jordan elimination | ||
| − | :*geometric representations | + | :*geometric representations, especially [[vector]]s |
*[[Linear transformations]] | *[[Linear transformations]] | ||
:*transformations, inverses and matrix products | :*transformations, inverses and matrix products | ||
| − | *[[ | + | *[[Determinant]]s |
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| − | |||
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| − | * | + | *[[Eigenvalue]]s |
| − | * | + | *[[Orthogonality]] |
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*Symmetry | *Symmetry | ||
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*Quadratic forms | *Quadratic forms | ||
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| + | More advanced topics include: | ||
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| + | *[[Linear spaces]] | ||
| + | :*isomorphisms | ||
| + | :*image and kernel | ||
| + | :*Nth dimensional spaces and subspaces | ||
==References== | ==References== | ||
Revision as of 02:01, April 24, 2010
Linear algebra is the mathematical subject that studies vectors, vector spaces, linear maps, and systems of linear equations. Branches of Linear algebra typically include Linear equations, Matrices, Matrix decompositions, Computations, Vectors, Vector spaces, Multilinear algebra, Affine space, Projective space.[1] Linear algebra has numerous applications in engineering, chemistry and physics.
A detailed list of the topics covered by a typical college-level course in Linear algebra are:
- coefficient matrices and Gauss-Jordan elimination
- geometric representations, especially vectors
- transformations, inverses and matrix products
- Symmetry
- Hermitian Matrices
- Linear differential equations
- Quadratic forms
More advanced topics include:
- isomorphisms
- image and kernel
- Nth dimensional spaces and subspaces