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Lecture
Linear Forms in Vector Spaces
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Related lectures (23)
Linear Algebra: Matrices and Vector Spaces
Covers matrix kernels, images, linear applications, independence, and bases in vector spaces.
Normed Spaces
Covers normed spaces, dual spaces, Banach spaces, Hilbert spaces, weak and strong convergence, reflexive spaces, and the Hahn-Banach theorem.
Vector Spaces: Properties and Operations
Covers the properties and operations of vector spaces, including addition and scalar multiplication.
Kernel, Image and Linear Maps
Explains kernel, image, and linear maps, illustrating concepts with examples.
Vector Spaces: Bases and Dimension
Explores bases, dimensions, and matrix ranks in vector spaces with practical examples and proofs.
Representation Theory: Algebras and Homomorphisms
Covers the goals and motivations of representation theory, focusing on associative algebras and homomorphisms.
Linear Algebra Basics
Covers the basics of linear algebra, emphasizing the identification of subspaces through key properties.
Vector Spaces Equivalence
Explores equivalence in vector spaces, covering conditions for statements to be considered equivalent and properties of algebraic bases.
Linear Independence and Bases in Vector Spaces
Explains linear independence, bases, and dimension in vector spaces, including the importance of the order of vectors in a basis.
Linear Independence and Bases
Covers linear independence, bases, and coordinate systems with examples and theorems.
Linear Applications: Definitions and Properties
Explores the definition and properties of linear applications, focusing on injectivity, surjectivity, kernel, and image, with a specific emphasis on matrices.
Vector Spaces: Sum of Subspaces
Covers the concept of the sum of vector subspaces in an IR-vector space.
Hermitian Forms: Definition and Properties
Explores the definition and properties of Hermitian forms in complex vector spaces.
Linear Transformations: Kernels and Images
Covers kernels and images of linear transformations between vector spaces, illustrating properties and providing proofs.
Orthogonality and Projection
Covers orthogonality, scalar products, orthogonal bases, and vector projection in detail.
Linear Algebra: Lecture Notes
Covers determining vector spaces, calculating kernels and images, defining bases, and discussing subspaces and vector spaces.
Orthogonality and Subspace Relations
Explores orthogonality between vectors and subspaces, demonstrating practical implications in matrix operations.
Vector Spaces: Linear Applications and Generators
Introduces vector spaces, linear applications, generators, and dimensionality in mathematics.
Linear Applications of Vector Spaces
Covers linear applications between vector spaces, exploring their properties and uniqueness based on bases.
Linear Transformations: Polynomials and Bases
Covers linear transformations between polynomial spaces and explores examples of linear independence and bases.
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