Lecture notes, 3.1-3.5.
- Cayley-Hamilton Theorem;
- Matrix exponentials;
- Solutions to linear systems differential equations.
Lecture notes, 3.1-3.5.
Mostly following Prasolov’s notes on linear algebra, chapter 1.
\(\def\Real{\mathbb{R}}\def\ee{\mathbf{e}}\def\ff{\mathbf{f}}\newcommand\ket[1]{\vert{#1}\rangle}\newcommand\bra[1]{\langle{#1}\vert}\newcommand\bk[2]{\langle #1\vert#2\rangle}\def\lin{\mathtt{Lin}} \)
\(\def\Real{\mathbb{R}}\def\ee{\mathbf{e}}\def\ff{\mathbf{f}}\newcommand\ket[1]{\vert{#1}\rangle}\newcommand\bra[1]{\langle{#1}\vert}\newcommand\bk[2]{\langle #1\vert#2\rangle}\def\lin{\mathtt{Lin}} \)
Continuing to use Olver’s book, chapter 1, but also relying on Prasolov’s notes on linear algebra.
Following lecture notes, 2.6, 2.7:
Continuing to use Olver’s book, chapter 1, but also relying on Prasolov’s notes on linear algebra.
\(\def\Real{\mathbb{R}}\def\ee{\mathbf{e}}\def\ff{\mathbf{f}}\newcommand\ket[1]{\vert{#1}\rangle}\newcommand\bra[1]{\langle{#1}\vert}\newcommand\bk[2]{\langle #1\vert#2\rangle}\def\lin{\mathtt{Lin}}\)
Still on Olver’s book, ch. 1.
Notion of (matrix) group: axioms – closedness, associativity, existence of unity, inverse.
Examples: groups of lower, upper triangular matrices. Matrix inverses.
Row swaps and permutation matrices. Group of permutation matrices.
Non-singular matrices and …
Practice exercise:
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