Loganallan
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Linear Algebra 2 - Orthogonal Matrices
Notes defining and covering theorems related to Orthogonal Matrices.
- Class notes
- • 4 pages •
Notes defining and covering theorems related to Orthogonal Matrices.
Linear Algebra 2 - Quadratic Forms on ℝ Vector Spaces
Notes discussing theorems for quadratic forms on ℝ vector spaces including rigorous proofs.
- Class notes
- • 4 pages •
Notes discussing theorems for quadratic forms on ℝ vector spaces including rigorous proofs.
Linear Algebra 2 - Hermitian Vector Spaces
Notes defining Hermitian forms on vector spaces, including various theorems that can be used when working with or finding them.
- Class notes
- • 16 pages •
Notes defining Hermitian forms on vector spaces, including various theorems that can be used when working with or finding them.
Linear Algebra 2 - Quadratic Forms on Euclidean Spaces: Algorithm of Finding a Canonical Basis
These notes go into more explicit detail on the practical algorithms for converting a quadratic form into canonical form. They also include a number of examples to help grasp it.
- Class notes
- • 22 pages •
These notes go into more explicit detail on the practical algorithms for converting a quadratic form into canonical form. They also include a number of examples to help grasp it.
Linear Algebra 2 - Canonical Form of a Quadratic and a Bilinear Form
We have previously defined both Quadratic and Bilinear Forms. This set of notes covers the process for converting these to Canonical Form.
- Class notes
- • 11 pages •
We have previously defined both Quadratic and Bilinear Forms. This set of notes covers the process for converting these to Canonical Form.
Linear Algebra 2 - Euclidean Vector Spaces
Notes defining Euclidean Vector Spaces, Gram Matrices and Orthogonal Matrices; with examples of each. Also includes a proof of the Cauchy-Bunyakovsky-Schwarz Inequality.
- Class notes
- • 13 pages •
Notes defining Euclidean Vector Spaces, Gram Matrices and Orthogonal Matrices; with examples of each. Also includes a proof of the Cauchy-Bunyakovsky-Schwarz Inequality.
Linear Algebra 2 - Bilinear Forms
Notes defining Bilinear Forms, Matrices of Bilinear Forms and Coordinate Representations. Covers concepts such as Rank, Symmetric and Skew-Symmetric Matrices, and Congruence.
- Class notes
- • 10 pages •
Notes defining Bilinear Forms, Matrices of Bilinear Forms and Coordinate Representations. Covers concepts such as Rank, Symmetric and Skew-Symmetric Matrices, and Congruence.
Linear Algebra 2 - Functions of Matrices
Notes on solving Cauchy problems using matrix concepts such as matrix powers, diagonalisability and eigenspaces. Includes various examples including the Fibonacci sequence.
- Class notes
- • 12 pages •
Notes on solving Cauchy problems using matrix concepts such as matrix powers, diagonalisability and eigenspaces. Includes various examples including the Fibonacci sequence.
Linear Algebra 1 - Complete Notes
The full set of lecture notes for Linear Algebra 1 which I used to earn 87% in the module.
- Package deal
- • 8 items •
- Linear Algebra 1 - Subspaces • Class notes
- Linear Algebra 1 - Systems of Linear Equations • Class notes
- Linear Algebra 1 - Vector Spaces • Class notes
- Linear Algebra 1 - Cayley-Hamilton Theorem • Class notes
- Linear Algebra 1 - Rank of a Matrix • Class notes
- And more ….
The full set of lecture notes for Linear Algebra 1 which I used to earn 87% in the module.
Linear Algebra 1 - Linear Maps
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.
- Class notes
- • 27 pages •
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.