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Systems of linear equations | definition of vector, algebraic structures of vector space | ![]() |
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Systems of linear equations | pivots, ranks, free variables, augmented matrix, Gaussian elimination | ![]() |
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Systems of linear equations | Gauss-Jordan elimination | ![]() |
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Systems of linear equations | existence and uniqueness of systems of linear equations, floating-point number,partial pivoting,ill- conditioned system | ![]() |
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matrix multiplication, matrix inverse | full column rank, full row rank, left inverse, right inverse, two-sided inverse | ![]() |
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matrix multiplication, matrix inverse | one-to-one (injective) mapping, onto(surjective) mapping, bijective mapping, Fredholm alternative | ![]() |
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matrix multiplication, matrix inverse | Gauss-Jordan elimination by block matrics, Sherman_Morrison_Woodbury formula | ![]() |
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vector space | span,linear dependent and independent, basis, dimensions, transition matrix (changes of basis) | ![]() |
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vector space | column space, basic columns, full rank factorization, Vandemonde matrices | ![]() |
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determinants | permutations, transpositions, parity, minors, cofactors, determinant of triangular matrices | ![]() |
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determinants | Cramer's rule,determinants calculation by block matrices | ![]() |
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determinants, cross products | cross product, Vandermonde determinant | ![]() |
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Linear transformation | More about rank, Linear transformation | ![]() |
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Linear transformation | Linear transformation, Adjoint operator | ![]() |
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Linear transformation | Transposed matrix, Symmetric matrix, self-adjoint-operator | ![]() |
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Linear transformation | Four fundamental subspaces | ![]() |
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Inner product space | orthogonal projection,Gram Schmidt algorithm, QR decomposition, revised Gram Schmidt algorithm | ![]() |
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Inner product space | overdetermined systems, method of least squares, underdetermined system, minimum norm problems | ![]() |
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Eigenvalue problems | eigenvalues, eigenvectors, characteristic polynomials, characteristic equations | ![]() |
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Eigenvalue problems | Spectral theorem, Cayley-Hamilton theorem, Self-adjoint operators, Unitary operator, Hermitian operators | ![]() |
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Eigenvalue problems | Sylvesters formula, difference equations, Fibonacci numbers, dfferential equations | ![]() |
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Eigenvalue problems | Differential Equations (Boundary value problems), Toeplitz matrices, Tridiagonal matrices, Boundary Conditions | ![]() |
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Eigenvalue problems | Normal Modes of Oscillation, Bilinear Forms, Quadratic Forms, Quadratic Equations, Conic Sections, Positive Definite Forms | ![]() |
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Singular Value Decomposition | SVD (Singular Value Decomposition), Pseudoinverse, Algebraic Multiplicity, Geometric Mulitiplicity | ![]() |