Linear algebra
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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
- Subspaces
- Symmetry
- Hermitian Matrices
- Linear differential equations
- Quadratic forms
More advanced topics include:
- isomorphisms
- image and kernel
- Nth dimensional spaces and subspaces
Common problems
Common problems in linear algebra include:
- simplifying or reducing matrices
- Gauss-Jordan elimination
- matrix multiplication
- finding inverses and transposes of matrices
- Gram-Schmidt process