In this video, we will show how matrices as computational tools may conveniently represent the action of a linear transformation upon a given basis. We will prove that conventional matrix operations, particularly matrix multiplication, conform to the composition of linear transformations. We will also cover 'change of basis' and show that the determinant is intrinsic to a linear transformation and independent of basis choice. We will then introduce the adjoint operator, which relates to the matrix (conjugate) transpose and give the definition of symmetric, anti-symmetric, and orthogonal transformations.
Patreon: / mathoma
Geometric Algebra playlist: • Geometric Algebra
References / Further Reading:
1. Lasenby and Doran's "Geometric Algebra for Physicists". www.amazon.com...
2. "A Survey of Geometric Algebra and Geometric Calculus" by Alan Macdonald: www.faculty.lut...
3. "Synopsis of Geometric Algebra" and "Geometric Calculus" by David Hestenes: geocalc.clas.as...
4. "New Foundations for Classical Mechanics" by David Hestenes: www.amazon.com...
Music:
J.S. Bach's Brandenberg Concerto No. 2 in F major, 1st mov.
Негізгі бет Geometric Algebra - The Matrix Representation of a Linear Transformation
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