Linear Algebra: Properties of Injective and Surjective Functions

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Mapping Functions and Surjections

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

Algebraic Identities and Trigonometry

Covers algebraic identities, trigonometry, and real functions, including injective, surjective, bijective, and reciprocal functions.

Linear Algebra: Bijections and Cardinality

Explores bijections in linear algebra and the concept of cardinality between sets.

Cartesian Products and Equivalence Relations

Introduces Cartesian products, equivalence relations, and functions, emphasizing the importance of order and discussing injective, surjective, and bijective functions.

Linear Transformations: Matrices and Applications

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

Bijective Functions

Introduces bijective functions, which are both injective and surjective, emphasizing one-to-one correspondence between domain and codomain.

Linear Algebra: Injective Functions

Focuses on injective functions in linear algebra, demonstrating how to verify properties and prove injectivity.

Proofs and Sets: Applications

Covers the basics of proofs, defining sets, and applications between sets.

Sets and Functions

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

Linear Algebra: Injective Functions

Explores injective functions in linear algebra, demonstrating how to prove injectivity step by step.