MATLAB Mathematics - SERC - Index of

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Contents 1 Matrices and Linear Algebra Function Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-2 Matrices in <strong>MATLAB</strong> . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-4 Creating Matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-4 Adding and Subtracting Matrices . . . . . . . . . . . . . . . . . . . . . . . 1-6 Vector Products and Transpose . . . . . . . . . . . . . . . . . . . . . . . . . 1-7 Multiplying Matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-8 The Identity Matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-10 The Kronecker Tensor Product . . . . . . . . . . . . . . . . . . . . . . . . . 1-11 Vector and Matrix Norms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-12 Solving Linear Systems <strong>of</strong> Equations . . . . . . . . . . . . . . . . . . 1-13 Computational Considerations . . . . . . . . . . . . . . . . . . . . . . . . . 1-13 General Solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-15 Square Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-15 Overdetermined Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-18 Underdetermined Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-20 Inverses and Determinants . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-22 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-22 Pseudoinverses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-23 Cholesky, LU, and QR Factorizations . . . . . . . . . . . . . . . . . . 1-27 Cholesky Factorization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-27 LU Factorization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-29 QR Factorization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-30 Matrix Powers and Exponentials . . . . . . . . . . . . . . . . . . . . . . 1-34 Eigenvalues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-38 Singular Value Decomposition . . . . . . . . . . . . . . . . . . . . . . . . 1-42 i
Page 1 and 2: MATLAB® The Language of Technical
Page 3: Revision History June 2004 First pr
Page 7 and 8: Function Summary . . . . . . . . .
Page 9 and 10: 6 Sparse Matrices Function Summary
Page 11 and 12: 1 Matrices and Linear Algebra Funct
Page 13 and 14: Function Summary Function Summary (
Page 15 and 16: Matrices in MATLAB The second examp
Page 17 and 18: Matrices in MATLAB Vector Products
Page 19 and 20: Matrices in MATLAB A = pascal(3); B
Page 21 and 22: Matrices in MATLAB returns an m-by-
Page 23 and 24: Solving Linear Systems of Equations
Page 33 and 34: Inverses and Determinants Again, be
Page 35 and 36: Inverses and Determinants The solut
Page 37 and 38: Cholesky, LU, and QR Factorizations
Page 45 and 46: Matrix Powers and Exponentials Y =
Page 47 and 48: Matrix Powers and Exponentials 1.2
Page 49 and 50: Eigenvalues The real part of each o
Page 51 and 52: Eigenvalues Schur Decomposition in
Page 53 and 54: Singular Value Decomposition For th
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2 Polynomials and Interpolation Pol
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Polynomials Polynomial Function Sum
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Polynomials Convolution and Deconvo
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Polynomials Compute the values of t
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Interpolation Interpolation Interpo
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Interpolation the relevant function
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Interpolation processing. Use bicub
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Interpolation 7 Compare the contour
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Interpolation are the points for wh
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Interpolation Functions for Analysi
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Interpolation You can use triplot t
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Interpolation 0 −1000 Depth in Fe
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Interpolation enclosing triangle fo
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Interpolation Functions for Multidi
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Interpolation Delaunay Tessellation
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Interpolation You can use cameramen
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Interpolation In this example, V is
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Interpolation The next step is to u
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Selected Bibliography Selected Bibl
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3 Fast Fourier Transform (FFT) Intr
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Introduction which results in y = 6
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Introduction Periodogram 2 x 107 cy
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Magnitude and Phase of Transformed
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FFT Length Versus Speed FFT Length
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4 Function Functions Function Summa
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Representing Functions in MATLAB Re
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Plotting Mathematical Functions Plo
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Plotting Mathematical Functions 100
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Minimizing Functions and Finding Ze
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Numerical Integration (Quadrature)
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Numerical Integration (Quadrature)
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Parameterizing Functions Called by
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5 Differential Equations Initial Va
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Initial Value Problems for ODEs and
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Initial Value Problems for DDEs Ini
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Initial Value Problems for DDEs Usi
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Initial Value Problems for DDEs For
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Initial Value Problems for DDEs dyd
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Initial Value Problems for DDEs Dis
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Initial Value Problems for DDEs The
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Boundary Value Problems for ODEs Bo
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Boundary Value Problems for ODEs No
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Boundary Value Problems for ODEs It
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Boundary Value Problems for ODEs so
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Boundary Value Problems for ODEs 6
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Boundary Value Problems for ODEs pr
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Boundary Value Problems for ODEs ne
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Boundary Value Problems for ODEs Fa
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Boundary Value Problems for ODEs It
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Boundary Value Problems for ODEs 5.
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Partial Differential Equations Part
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Partial Differential Equations equa
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Partial Differential Equations bcfu
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Partial Differential Equations At x
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Partial Differential Equations ql =
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Partial Differential Equations b Di
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Partial Differential Equations The
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Partial Differential Equations 5 Se
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Partial Differential Equations u2(x
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6 Sparse Matrices Function Summary
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Function Summary Function Summary (
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Introduction Introduction Sparse ma
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Introduction whos Name Size Bytes C
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Introduction (3,2) 3 (4,3) 4 (1,4)
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Introduction d = [-3 0 2]; Use thes
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Viewing Sparse Matrices Viewing Spa
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Viewing Sparse Matrices Note that i
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Adjacency Matrices and Graphs Adjac
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Adjacency Matrices and Graphs To ob
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Adjacency Matrices and Graphs 0 10
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Adjacency Matrices and Graphs An Ai
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Sparse Matrix Operations Sparse Mat
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Sparse Matrix Operations For exampl
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Sparse Matrix Operations The functi
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Sparse Matrix Operations selects P
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Sparse Matrix Operations Cuthill-Mc
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Sparse Matrix Operations It is also
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Sparse Matrix Operations preorderin
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Sparse Matrix Operations Background
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Sparse Matrix Operations Performanc
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Sparse Matrix Operations Using line
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Index A additional parameters BVP e
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Index displaying sparse matrices 6-
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Index linear transformation 1-4 loa
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Index P Partial Differential Equati
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Index reordering 6-26 storage 6-5 f
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