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Antilinear map
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Exam Q10 solution
Discusses the misconception that an injective linear map must have M strictly smaller than N.
Diagonalization of Matrices and Least Squares
Covers diagonalization of matrices, eigenvectors, linear maps, and least squares method.
Singular Values and Norms: Understanding Linear Maps with SVD
Explores singular value decomposition and its role in understanding linear maps.
Linear Maps: Dimension and Bases
Explores the dimension of linear maps and the construction of bases.
Linear Applications: Matrices and Properties
Explores linear applications, matrices, injectivity, surjectivity, and compositions of linear maps with examples and demonstrations.
Linear Maps and Bases: The Rank Theorem
Covers bijective linear maps, invertibility of matrices, isomorphisms, and the rank theorem.
Vector Spaces: Definitions and Applications
Introduces vector spaces, subspaces, linear maps, and evaluation maps, with examples and exercises for better comprehension.
Complex Functions: Linear and Anti-linear
Covers complex functions, linear and anti-linear functions, harmonic polynomials, rational functions, and exponential functions.
Tensor Products and Symmetric Power
Covers tensor products, symmetric power, and exterior power of vector spaces, including properties and applications.
The Regular Representation
Introduces the regular representation, a key tool for studying group actions on varieties.