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.
Basic Concepts
- coefficient matrices and Gauss-Jordan elimination
- geometric representations, especially vectors
- transformations, inverses and matrix products
- Subspaces
- eigenbasis
- orthogonal eigenbasis
- orthonormal eigenbasis
- Symmetric matrix
- Quadratic forms
- Linear dynamical systems
- Euler's Formula
More advanced topics include
- Vector spaces (linear spaces)
- the conditions of a vector space
- isomorphisms
- Nth dimensional spaces and subspaces
- Inner spaces
- inner product spaces
- Hermitian Matrices
- Singular values and Singular Value Decomposition
- Linear differential equations
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 procedure
- finding eigenvalues and eigenvectors for matrices