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Linear Algebra in Mathematica

1. Introduction Tensors and Arrays Matrices as Mathematica Expressions Design Principles of Mathematica

2. Matrix and Tensor Operations Building Matrices Structural Operations Element-wise Operations Vectors and Tensors Visualization of Matrices Import and Export of Matrices Matrix Multiplication Matrix Permutations

3. Sparse Arrays Basic Operations Structural Operations Element-wise Operations Visualization of Sparse Matrices Import and Export of Sparse Matrices Matrix Multiplication Matrix Permutations Converting Equations to Sparse Arrays SparseArray Data Format

4. Matrix Computations Basic Operations Solving Linear Systems Least Squares Solutions Eigensystem Computations Matrix Decompositions Functions of Matrices

5. Matrix Types Numbers in Mathematica Matrices in Mathematica Complex Matrices Arbitrary-Precision Matrices

6. Performance Packed Arrays Programming Efficiency Expression Efficiency

7. Examples Matrix Ordering Full Rank Least Squares Solutions Minimization of 1 and Infinity Norms Finite Difference Solutions Mesh Partitioning Matrix Functions with NDSolve

8. Appendix Software References References