Rank Theorem: Matrix Dimension and Subspaces

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Explores the properties of invertible matrices, including unique solutions and linear independence.

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

Covers linear algebra basics, including matrices, change of basis, and invertible matrices.

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

Covers LU factorization, linear independence, and matrix equations.

Explores matrix similarity, diagonalization, characteristic polynomials, eigenvalues, and eigenvectors in linear algebra.

Explores linear combinations of vectors and matrices in Rn, demonstrating geometric interpretations and matrix operations.

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.

Explores forming bases, dependencies, and relationships in linear applications using invertible matrices and canonical bases.