Linear Algebra 1 (MAA142)

Notes defining and giving examples of linear maps. Also includes elementary operations for linear maps as well as introducing the concept of Kernels and Images and the Rank-Nullity Formula for linear maps.

Notes defining vector spaces and linear combinations for linear algebra. Includes all theorems required for the module section as well as examples and diagrams.

Notes covering the rules of matrix algebra including the elementary operations, transposition and inverting a matrix.

Notes on how to find the determinant of an nxn matrix. Includes a number of theorems related to the determinant of a matrix as well as the effects of the determinant under elementary operations.

Notes on subspaces of vector spaces including examples, their operations, respective theorems and propositions as well as visual representations.

Notes on how to find the eigenvalues and eigenvectors of a matrix as well as how to determine whether a matrix is diagonalisable.

Definitions of rank and minors of a matrix with all associated theorems needed for this section of Linear Algebra 1.

Notes on the Cayley-Hamilton Theorem in Linear Algebra with its corollary and a rigorous proof.

Notes on methods of solving systems of linear equations (or simultaneous equations including the Gauss Elimination Method.