Linear Algebra 2 (MAA241)
Loughborough University (LU)
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Linear Algebra 2 - Hermitian Vector Spaces
- Lecture notes • 16 pages • 2022
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Notes defining Hermitian forms on vector spaces, including various theorems that can be used when working with or finding them.
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Linear Algebra 2 - Bilinear Forms
- Lecture notes • 10 pages • 2022
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Notes defining Bilinear Forms, Matrices of Bilinear Forms and Coordinate Representations. Covers concepts such as Rank, Symmetric and Skew-Symmetric Matrices, and Congruence.
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Linear Algebra 2 - Euclidean Vector Spaces
- Lecture notes • 13 pages • 2022
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Notes defining Euclidean Vector Spaces, Gram Matrices and Orthogonal Matrices; with examples of each. Also includes a proof of the Cauchy-Bunyakovsky-Schwarz Inequality.
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Linear Algebra 2 - Quadratic Forms on Euclidean Spaces: Algorithm of Finding a Canonical Basis
- Lecture notes • 22 pages • 2022
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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.
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Linear Algebra 2 - Functions of Matrices
- Lecture notes • 12 pages • 2022
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Notes on solving Cauchy problems using matrix concepts such as matrix powers, diagonalisability and eigenspaces. Includes various examples including the Fibonacci sequence.
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Linear Algebra 2 - Canonical Form of a Quadratic and a Bilinear Form
- Lecture notes • 11 pages • 2022
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We have previously defined both Quadratic and Bilinear Forms. This set of notes covers the process for converting these to Canonical Form.
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Linear Algebra 2 - Orthogonal Matrices
- Lecture notes • 4 pages • 2022
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Notes defining and covering theorems related to Orthogonal Matrices.
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Linear Algebra 2 - Quadratic Forms on ℝ Vector Spaces
- Lecture notes • 4 pages • 2022
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Notes discussing theorems for quadratic forms on ℝ vector spaces including rigorous proofs.
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