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Antilinear map
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Linear Applications: Bases and Dual Spaces
Explores bases, dual spaces, and linear applications in linear algebra.
Comparing Tangent Vectors: Parallel Transport
Explores the definition, existence, and uniqueness of parallel transport of tangent vectors on manifolds.
Linear Maps and the Duality Principle in Mathematics
Covers the duality principle in linear algebra and its implications in mathematics.
Group representations constructions
Explores the construction of group representations through various methods and provides an illustrative example using the standard representation of sr2 on c2.
Isometries in R^2 and R^3
Explores isometries in R^2 and R^3, focusing on symmetries, rotations, and linear compositions, with a glimpse into the Banach-Tarski paradox.
2D Transformations: Linear Maps & Matrices
Covers 2D transformations, linear maps, matrices, affine transformations, and orthogonal transformations.
Isometries: Definition and Examples
Explores isometries, distinguishing between rotations and reflections, and the preservation of orientation in geometric transformations.
Advanced Linear Algebra: Matrices Conjugation and Equivalence
Explores matrices conjugation, equivalence, and similarity in advanced linear algebra.
Kernel, Image and Linear Maps
Explains kernel, image, and linear maps, illustrating concepts with examples.
Matrix Representations: Linear Maps
Explores matrix representations of linear maps and their invariance, using examples and special cases.