Matrix Recurrence Relations

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Diagonalization of Matrices and Least Squares

Explores diagonalization of matrices, similarity relations, and eigenvectors in linear algebra.

Eigenvalues and Eigenvectors: Understanding Matrices

Explores eigenvalues and eigenvectors in matrices through examples and calculations.

Linear Algebra: Canonical Basis

Explores the canonical basis in linear algebra, focusing on matrix representation, diagonalizability, and characteristic polynomials.

Matrix Similarity and Diagonalization

Explores matrix similarity, eigenvalues, and diagonalization in linear algebra.

Fibonacci numbers and the golden ratio

Explores the Fibonacci sequence, identities, golden ratio, and explicit formulas.

Linear Algebra Basics: Vector Spaces, Transformations, Eigenvalues

Covers fundamental linear algebra concepts like vector spaces and eigenvalues.

Advanced Counting: Examples

Covers advanced counting techniques, including linear recurrence relations and generating functions, with examples from the Fibonacci sequence and differences between dice and poker cards.

Non-Diagonalizable Case: Two Eigenvalues (Example)

Showcases a non-diagonalizable matrix example and explores eigenvalues and eigenvectors.

Eigenvalues and Eigenvectors

Explores eigenvalues, eigenvectors, and methods for solving linear systems with a focus on rounding errors and preconditioning matrices.

Diagonalization of Matrices: Theory and Examples

Covers the theory and examples of diagonalizing matrices, focusing on eigenvalues, eigenvectors, and linear independence.