review of linear algebra - donald bren school of
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Review of Linear Algebra
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Solving systems of linear equations
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Elementary row operations
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Row echelon form
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Complexity of Gaussian elimination: O(n3)
Iterative (approximate) methods
Basic idea: splitting A into M - N where M is invertible. Then
Mx = Nx + b
Iterate: x M-1(Nx+b)
Vector Space
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Subspace
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Rank Theorem
For any m x n matrix A:
rk(A) + dim Null(A) = n
Num of pivot columns + num of nonpivot columns = num of columns
Fundamental theorem of linear mapping
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