Algebra of linear maps over vector spaces.
References
Based on \cite{strang}, \cite{trefBau}, \cite{hornJohnson} \cite{hornJohnsonTopics}, \cite{matrixCookbook}.
Linear algebra over field F
Vector space over field F with all linear transformations.
Themes
Linear transformations and matrices; their properties. Systems of linear equations. Using decompotions to understand the operation of linear maps better.
Related surveys
For info on vectors, vector spaces, various functionals (including norms), non-linear functions: see survey of vector spaces, their functions and functionals.
For numerical analysis, conditioning, stability, differnce equations, differential equations: see Numerical analysis ref.
Characterization of research effort
See algorithms ref; Both strategies mentioned there are useful.
Experiment with Matlab.
Matrix algorithm design
The decompoisitional approach to matrix computations is extremely useful. Think of a computation in terms of triangular, diagonal, orthogonal etc.. decompositions. Facilitates error analysis.
Working with algebra
Invlolves much algebra in addition. Reasoning about matrix operations: Understand what is going on by the use of algebra; eg: write scaling rows of
Use induction a lot.
Also see algebra/ mathematical structures ref.
Notes
- ky Fan norms here.