Linear Algebra - Lecture 39: The Characteristic Polynomial and Multiplicity
Автор: Nathaniel Johnston
Загружено: 2021-03-17
Просмотров: 3442
Описание:
We talk about the characteristic polynomial of a matrix, and what polynomials can tell us about eigenvalues. We also introduce the algebraic and geometric multiplicities of an eigenvalue, and we talk about why the eigenvalues of a triangular matrix are its diagonal entries.
Textbook: http://www.njohnston.ca/publications/...
Blank course notes (lectures 37-39): http://www.njohnston.ca/la_week10.pdf
Annotated course notes (lectures 37-39): http://www.njohnston.ca/la_week10_ann...
Please leave a comment below if you have any questions, comments, or corrections.
Timestamps:
00:00 - Introduction and definition
03:08 - 3x3 example
09:47 - Algebraic and geometric multiplicities
15:20 - The Fundamental Theorem of Algebra (sum of algebraic multiplicities)
20:25 - Eigenvalues of triangular matrices
#linearalgebra #eigenvaluesandeigenvectors #matrices #math
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