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Lecture
Linear Applications: Definitions and Examples
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Linear Transformations: Matrices and Applications
Covers linear transformations using matrices, focusing on linearity, image, and kernel.
Linear Applications: Matrices and Transformations
Covers linear applications, matrices, transformations, and the principle of superposition.
Spherical Tensors and Wigner-Eckart Theorem
Covers the transformation of vectors and tensors in quantum physics.
Linear Algebra: Subspaces and Transformations
Explores subspaces in linear algebra and transformations, including kernels and images of linear transformations.
Linear Algebra: Change of Basis Matrices
Explores change of basis matrices in linear algebra, emphasizing the importance of understanding matrix transformations between different bases.
Galilean Transformations: Spacetime and Measurements
Explores Galilean transformations in spacetime, focusing on measurements and coordinate transformations.
Elements of Lie Groups and Algebras
Explores the transformation of vectors and tensors in quantum physics, emphasizing Lie groups and algebras.
Properties of Fourier Transform
Explores the properties and applications of the Fourier transform in signal processing and mathematics.
Isometries: Definition and Examples
Explores isometries, distinguishing between rotations and reflections, and the preservation of orientation in geometric transformations.
Isometries in Euclidean Spaces
Explores isometries in Euclidean spaces, including translations, rotations, and linear symmetries, with a focus on matrices.