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Watch the 1st video of the course
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Lecture 1: The Geometry of Linear Equations.
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Lecture 2: Elimination with Matrices.
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Lecture 3: Multiplication and Inverse Matrices.
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Lecture 4: Factorization into A = LU
There is finally a better version of this lecture! https://www.youtube.com/watch?v=MsIvs_6vC38&index=4&list=PLE7DDD91010BC51F8
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Lecture 5: Transposes, Permutations, Spaces R^n.
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Lecture 6: Column Space and Nullspace.
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Lecture 7: Solving Ax = 0: Pivot Variables, Special Solutions.
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Lecture 8: Solving Ax = b: Row Reduced Form R.
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Lecture 9: Independence, Basis, and Dimension.
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Lecture 10: The Four Fundamental Subspaces.
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Lecture 11: Matrix Spaces; Rank 1; Small World Graphs.
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Lecture 12: Graphs, Networks, Incidence Matrices.
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Lecture 13: Quiz 1 Review.
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Lecture 14: Orthogonal Vectors and Subspaces.
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Lecture 15: Projections onto Subspaces.
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Lecture 16: Projection Matrices and Least Squares.
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Lecture 17: Orthogonal Matrices and Gram-Schmidt.
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Lecture 18: Properties of Determinants.
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Lecture 19: Determinant Formulas and Cofactors.
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Lecture 20: Cramer's Rule, Inverse Matrix, and Volume.
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