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Matrices (Metric)
Class Details
Tom Baker
Learn, or revise, determinants, matrix inverses, Gaussian elimination and eigenvalues/eigenvectors.
Units
Determinants
Determinant of 2 by 2 and 3 by 3 matrices (a Further Maths topic). Cramer's Rule (a First Year university topic).
Inverses
Inverse of 2 by 2 and 3 by 3 matrices (a Further Maths topic).
Gaussian Elimination
Solving systems of equations using Gaussian elimination and LU factorisation; matrix inversion using Gauss-Jordan elimination. A First Year university topic.
Eigenvalues and Eigenvectors
Eigenvalues and eigenvectors of square matrices. You may possible have met this if you've done Further Maths or the equivalent.
Diagonalisation of a square matrix; the diagonal matrix of eigenvalues and the diagonalising matrix of eigenvectors.
The normalised eigenvectors of a symmetric matrix are orthonormal.
How to tell whether a matrix can be diagonalised.
A square matrix satisfies its own characteristic equation; using this fact to calculate powers and inverses.