PRODUCTS
Products Overview
Mathematica
Mathematica Student Edition
Mathematica Home Edition
Wolfram
CDF Player
(free download)
Computable Document Format (CDF)
web
Mathematica
grid
Mathematica
Wolfram
Workbench
Wolfram
SystemModeler
Wolfram
Finance Platform
Mathematica
Add-Ons
Wolfram|Alpha Products
SOLUTIONS
Solutions Overview
Engineering
Aerospace Engineering & Defense
Chemical Engineering
Control Systems
Electrical Engineering
Image Processing
Industrial Engineering
Materials Science
Mechanical Engineering
Operations Research
Optics
Petroleum Engineering
Biotechnology & Medicine
Bioinformatics
Medical Imaging
Finance, Statistics & Business Analysis
Actuarial Sciences
Data Analysis & Mining
Econometrics
Economics
Financial Engineering & Mathematics
Financial Risk Management
Statistics
Software Engineering & Content Delivery
Authoring & Publishing
Interface Development
Software Engineering
Web Development
Science
Astronomy
Biological Sciences
Chemistry
Environmental Sciences
Geosciences
Social & Behavioral Sciences
Design, Arts & Entertainment
Game Design, Special Effects & Generative Art
Education
STEM Education Initiative
Higher Education
Community & Technical College Education
Primary & Secondary Education
Students
Technology
Computable Document Format (CDF)
High-Performance & Parallel Computing (HPC)
See Also: Technology Guide
PURCHASE
Online Store
Other Ways to Buy
Volume & Site Licensing
Contact Sales
Software
Service
Upgrades
Training
Books
Merchandise
SUPPORT
Support Overview
Mathematica
Documentation
Knowledge Base
Learning Center
Technical Services
Community & Forums
Training
Does My Site Have a License?
Wolfram User Portal
COMPANY
About Wolfram Research
News
Events
Wolfram Blog
Partnerships
Employment Opportunities
History of
Mathematica
Stephen Wolfram's Home Page
Contact Us
OUR SITES
All Sites
Wolfram|Alpha
Demonstrations Project
MathWorld
Integrator
Wolfram Functions Site
Mathematica Journal
Wolfram Media
Wolfram
Tones
Wolfram Science
Stephen Wolfram
SEARCH MATHEMATICA 8 DOCUMENTATION
THIS IS DOCUMENTATION FOR AN OBSOLETE PRODUCT.
SEE THE
DOCUMENTATION CENTER
FOR THE LATEST INFORMATION.
Mathematica
>
Mathematica
Overview
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
© 2013 Wolfram Research, Inc.