I am reading the text book "Linear Algebra a geometric approach "by S Kumaresan. It says that a non-empty subset $S $ of Vector space $V $ is an affine space iff it is of the form $v+W $ for some $v \in V $ and a vector subspace $W $ of $V$.Now my confusion is that the definition of Quotient space says exactly same thing! Does they are same thing if yes why they are distinguished by distinct names. We know affine space my not a subspace but still $dim v+W =dim W$. How does one can define dimension of nonvector space? Thanks for reading.
Linear Algebra A Geometric Approach By S Kumaresan [HOT]
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This course covers a variety of methods for image representation, analysis, enhancement and compression. Color spaces, geometric projections and transformations. Multidimensional signals and systems: Fourier analysis, sampling, filtering. Transforms (e.g., DCT and wavelet). Gibbs-Markov random fields, Bayesian methods, information theoretic methods. Multiresolution schemes (e.g., pyramidal coding). Morphological and nonlinear methods. Edges, boundaries and segmentation. Applications of PDEs (e.g., anisotropic diffusion). Compressive sensing. Technical readings and projects in MATLAB (or other suitable language).
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Finite-dimensional vector spaces. Linear independence. Dimension. Basis. Subspaces. Inner product. Matrices. Rank. Determinant. Systems of linear equations. Matrix algebra. Coordinate transformation. Orthogonal matrices. Linear transformation. Eigen values and eigen vectors. Quadratic forms. Canonical form.
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