Stellar

Introduction Coordinate vectors and dot products Systems of linear equations Gaussian elimination Matrices and operations Row echelon form Elementary matrices and decompositions Vector spaces Definitions and examples Subspaces and operations Span, independence and bases Dimension and Grassmann formula Notable vector spaces Affine geometry Affine spaces Affine subspaces and coordinates Linear maps and rank Linear transformations Kernel, image and invertibility Ranks Matrices of linear maps Error-correcting codes Duality, determinants and orientation Dual spaces Change of basis Determinants Orientation Objects Diagonalization Eigenvalues and eigenvectors Characteristic polynomial Diagonalization criteria Inner product spaces Inner products, norms and orthogonality Orthonormal bases and Gram-Schmidt Adjoints and spectral theorem Linear isometries Quadratic forms Advanced vector and affine geometry Cross product in R3 Affine maps Euclidean affine spaces Types of matrices Quotient spaces Sum and scalar product Dimension of quotient spaces Isomorphism theorems Tensor products Exercises Batch 1 Batch 2 Batch 3 Batch 4 Batch 5 Batch 6 Batch 7 Batch 8 Batch 9 Batch 10 Batch 11 Batch 12 Batch 13 Batch 14 Batch 15

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