Difference between revisions of "Linear algebra"
Jump to navigation
Jump to search
(more detail added) |
|||
| Line 1: | Line 1: | ||
| − | '''Linear algebra''' is the [[mathematical]] subject that studies [[vector]]s, vector spaces, linear maps, and systems of linear [[equation]]s. | + | '''Linear algebra''' is the [[mathematical]] subject that studies [[vector]]s, vector spaces, linear maps, and systems of linear [[equation]]s. Branches of Linear algebra typically include Linear equations, Matrices, [[Matrix]] decompositions, Computations, Vectors, Vector spaces, Multilinear algebra, Affine space, Projective space.<ref>[http://www.m-w.com/cgi-bin/dictionary?book=Dictionary&va=linear+algebra Merriam Webster definition of Linear Algebra]</ref> |
Linear algebra has numerous applications in [[engineering]], [[chemistry]] and [[physics]]. | 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: | ||
| + | |||
| + | *Linear equations | ||
| + | :*coefficient matrices and Gauss-Jordan elimination | ||
| + | :*geometric representations | ||
| + | |||
| + | *Linear transformations | ||
| + | :*transformations, inverses and matrix products | ||
| + | |||
| + | *Linear spaces | ||
| + | :*isomorphisms | ||
| + | :*image and kernel | ||
| + | :*Nth dimensional spaces and subspaces | ||
| + | |||
| + | *Determinants | ||
| + | |||
| + | *Eigenvalues | ||
| + | |||
| + | *Orthogonality | ||
| + | |||
| + | *Symmetry | ||
| + | |||
| + | *Linear differential equations | ||
| + | |||
| + | *Quadratic forms | ||
==References== | ==References== | ||
| Line 6: | Line 32: | ||
[[Category:Linear algebra]] | [[Category:Linear algebra]] | ||
| + | [[category:mathematics]] | ||
Revision as of 22:57, January 31, 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:
- Linear equations
- coefficient matrices and Gauss-Jordan elimination
- geometric representations
- Linear transformations
- transformations, inverses and matrix products
- Linear spaces
- isomorphisms
- image and kernel
- Nth dimensional spaces and subspaces
- Determinants
- Eigenvalues
- Orthogonality
- Symmetry
- Linear differential equations
- Quadratic forms