Linear Transformations: Matrices and Applications

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Related lectures (27)

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Linear Algebra: Subspaces and Transformations

Explores subspaces in linear algebra and transformations, including kernels and images of linear transformations.

Linear Algebra: Vector Spaces and Applications

Covers linear dependence, independence, and applications in vector spaces.

Linear Transformations: Matrices and Applications

Explores linear transformations, matrices, injective and surjective functions, and their applications.

Characterization of Invertible Matrices

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

Characteristic Polynomials and Similar Matrices

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

Linear Independence: Definition and Examples

Explores the concept of linear independence in vector spaces through definitions and illustrative examples.

Tangent vectors without embedding space: Making tangent spaces linear

Explores making tangent spaces linear, defining tangent vectors without an embedding space and their operations, as well as the equivalence of different tangent space notions.

Linear Transformations: Matrices and Applications

Explores linear transformations, matrices, injective, surjective, and bijective properties, matrix operations, and special matrix types.

Linear Algebra: Matrix Operations

Explores matrix operations, injectivity, surjectivity, column spaces, and linear applications in linear algebra.

Mapping Functions and Surjections

Explores mapping functions, surjections, injective and surjective functions, and bijective functions.