Expanding to Higher Dimensions

To get higher dimensional aggregates, you can create one-dimensional aggregates with elements that are themselves aggregates, for example, lists of list, one-dimensional arrays of list of multisets, and so on. For applications requiring two-dimensional homogeneous aggregates, you will likely find two-dimensional arrays and matrices useful. The entries in TwoDimensionalArray and Matrix objects are all the same type, except that those for Matrix must belong to a Ring. You create and access elements in roughly the same way. Since matrices have an understood algebraic structure, certain algebraic operations are available for matrices but not for arrays. Because of this, we limit our discussion here to Matrix, that can be regarded as an extension of TwoDimensionalArray. See TwoDimensionalArray For more information about Axiom's linear algebra facilities see Matrix, Permanent, SquareMatrix, Vector, Computation of Eigenvalues and Eigenvectors, and Solution of Linear and Polynomial Equations. You can create a matrix from a list of lists, where each of the inner lists represents a row of the matrix.

The "collections" construct (see Creating Lists and Streams with Iterators) is useful for creating matrices whose entries are given by formulas.

Let vm denote the three by three Vandermonde matrix.

Use this syntax to extract an entry in the matrix.

You can also pull out a row or a column.

You can do arithmetic.

You can perform operations such as transpose, trace, and determinant