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Linear Algebra in Mathematica
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MATHEMATICA OVERVIEW
Additional functionality related to this tutorial has been introduced in subsequent versions of
Mathematica
. For the latest information, see
Matrices and Linear Algebra
.
Linear Algebra in
Mathematica
Introduction
Tensors and Arrays
Matrices as
Mathematica
Expressions
Expression Input and Output
Design Principles of
Mathematica
Matrix and Tensor Operations
Building Matrices
Special Matrices
Structural Operations
Getting Pieces of Matrices
Getting Multiple Pieces
Setting Pieces of Matrices
Setting Multiple Pieces
Extracting Submatrices
Deleting Rows and Columns
Inserting Rows and Columns
Extending Matrices
Transpose
Rotating Elements
Testing Matrices
Further Structural Operations
Element-wise Operations
Listability
Map
Vectors and Tensors
Testing Vectors and Tensors
Visualization of Matrices
Formatting Matrices
Plotting Matrices
Import and Export of Matrices
Matrix Multiplication
Outer Product
Visualization of the Outer Product
Generalized Inner Product
Matrix Permutations
Permutation Matrices
Working with Sparse Arrays
Basic Operations
SparseArray
Rule Inputs for SparseArray
Banded Sparse Matrices
Identity and Diagonal Sparse Matrices
Normal
ArrayRules
Structural Operations
Getting Pieces of Matrices
Getting Multiple Pieces
Setting Pieces of Matrices
Setting Multiple Pieces
Extracting Submatrices
Deleting Rows and Columns
Inserting Rows and Columns
Extending Matrices
Transpose
Rotating Elements
Testing Matrices
Further Structural Operations
Element-wise Operations
Listability
Map
Visualization of Sparse Matrices
Formatting Sparse Matrices
Plotting Sparse Matrices
Import and Export of Sparse Matrices
Matrix Multiplication
Outer Product
Matrix Permutations
Converting Equations to Sparse Arrays
SparseArray Data Format
Matrix Computations
Basic Operations
Norms
Vector Norms
Matrix Norms
NullSpace
Rank
Reduced Row Echelon Form
Inverse
PseudoInverse
Determinant
Minors
Solving Linear Systems
Singular Matrices
Homogeneous Equations
Estimating and Calculating Accuracy
Symbolic and Exact Matrices
Row Reduction
Saving the Factorization
Methods
LAPACK
Multifrontal
Krylov
Cholesky
Symbolic Methods
Least Squares Solutions
Data Fitting
Eigensystem Computations
Eigensystem Properties
Diagonalizing a Matrix
Symbolic and Exact Matrices
Generalized Eigenvalues
Methods
LAPACK
Arnoldi
Symbolic Methods
Matrix Decompositions
LU Decomposition
Cholesky Decomposition
Cholesky and LU Factorizations
Orthogonalization
QR Decomposition
Solving Systems of Equations
Singular Value Decomposition
Generalized Singular Values
Options
Schur Decomposition
Generalized Schur Decomposition
Options
Jordan Decomposition
Functions of Matrices
Matrix Types
Numbers in
Mathematica
Exact versus Approximate Numbers
Mixed Mode Arithmetic
Matrices in
Mathematica
Standard Numerical Techniques
Arbitrary-Precision Numerical Techniques
Symbolic Algebra Techniques
Mixed Mode Matrices
Complex Matrices
Arbitrary-Precision Matrices
Performance of Linear Algebra Computation
Packed Arrays
Packed Array Functions
Packed Array Operations
Packed Array Summary
Programming Efficiency
Measuring Performance
Vectorizing Loops
List Creation
List Updating
Using Built-in Support
A Slow Way
A Faster Way
Also Fast but Neater
Matrix Contents
Mixed Symbolic/Numerical Matrices
Mixed Numerical Type Matrices
Integer Matrices
Expression Efficiency
Updating of Matrices
Appending to Matrices
Linear Algebra Examples
Matrix Ordering
Full Rank Least Squares Solutions
Least Squares Cholesky
Least Squares QR
Minimization of 1 and Infinity Norms
One-Norm Minimization
Infinity-Norm Minimization
Finite Difference Solutions
Mesh Partitioning
Data
Plotting the Mesh
The Laplacian
The Fiedler Vector
Partitioning the Nodes
Matrix Functions with NDSolve
References
Software References
ARPACK
ATLAS
Harwell-Boeing
Matrix Market
METIS
TAUCS
UMFPACK
Other References
TUTORIAL COLLECTION
Mathematics and Algorithms
