Matrix Equations and Homogeneous Systems

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Covers linear equations, vectors, and matrices, exploring their fundamental concepts and applications.

Explores matrix operations, linear systems, solutions, and the span of vectors in linear algebra.

Explores characteristic polynomials, similarity of matrices, and eigenvalues in linear transformations.

Covers linear applications, matrices, transformations, and the principle of superposition.

Explains the construction of U, verification of results, and interpretation of SVD in matrix decomposition.

Explains linear independence, basis, and matrix rank with examples and exercises.

Covers the properties and operations of vector spaces, including addition and scalar multiplication.

Introduces algebraic properties, vector equations, and matrix operations.

Explores the equivalence between different properties of linear transformations represented by matrices and various matrix operations.

Explains linear independence, bases, and dimension in vector spaces, including the importance of the order of vectors in a basis.