In this video, we will review some basic concepts from linear algebra, such as the linear transformation, prove important theorems which ground matrix operations, extend the linear transformation on vectors to higher-graded elements to bivectors and trivectors, and define the determinant of a linear transformation from the point of view of geometric algebra.
Geometric Algebra playlist: • Geometric Algebra
Patreon: / mathoma
References / Further Reading:
1. Lasenby and Doran's "Geometric Algebra for Physicists". www.amazon.com/Geometric-Alge...
2. "A Survey of Geometric Algebra and Geometric Calculus" by Alan Macdonald: www.faculty.luther.edu/~macdon...
3. "Synopsis of Geometric Algebra" and "Geometric Calculus" by David Hestenes: geocalc.clas.asu.edu/html/NFMP...
4. "New Foundations for Classical Mechanics" by David Hestenes: www.amazon.com/Foundations-Cl...
Music:
J.S. Bach's Brandenberg Concerto No. 2 in F major, 1st mov.
Негізгі бет Ғылым және технология Geometric Algebra - Linear Transformations, Outermorphism, and the Determinant
Пікірлер: 21