Linear Maps: Injectivity and Surjectivity

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Linear Transformations: Matrices and Applications

Explores linear transformations, matrices, surjective, injective, and bijective properties, symmetric transformations, and matrix equivalence.

Linear Applications: Matrices and Properties

Explores linear applications, matrices, injectivity, surjectivity, and compositions of linear maps with examples and demonstrations.

Function Properties: Injective, Surjective, Bijective

Explains injective, surjective, and bijective functions using examples and graphs.

Linear Transformations: Matrices and Applications

Explores linear transformations, matrices, and their properties, including surjectivity, injectivity, and symmetry operations.

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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 Applications: Definitions and Properties

Covers linear applications, including definitions, properties, and examples.

Linear Algebra: Matrix Operations

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

Mathematical Analysis: Functions and Composition

Covers the analysis of functions, composition, and mathematical induction.

Sets and Functions

Introduces sets, functions, and their properties, including injective and surjective functions, composition, and inverse functions.