Linear Algebra: The Rank Theorem

Related lectures (24)

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

Covers fundamental concepts in linear algebra, including linear equations, matrix operations, determinants, and vector spaces.

Covers matrix kernels, images, linear applications, independence, and bases in vector spaces.

Covers linear independence, bases, and coordinate systems with examples and theorems.

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

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

Introduces orthogonal families, orthonormal bases, and projections in linear algebra.

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

Explores bases, dimensions, and matrix ranks in vector spaces with practical examples and proofs.

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