Matrix Library

• 1. Initialization
• 2. Functions
• 3. Future Revisions
• 4. References

The Matrix Library

This library implements some basic matrix operations. These functions are not guarenteed to be stable or numerically sound, nor are they very optimized, but for smaller applications they should be suitable.

The <matrix> class is a subclass of <array>, so all operations on <array>s and collections in general should work as expected. One important limitation of matrices is that they are limited to two dimensions, and trying to use any other size results in an error.

1. Initialization

The generic function make will create matrices, with two keywords:

dimensions: a sequence of two elements which represent the rows and columns of the matrix respectively

fill: the objects that each element of matrix should be initialized to. This defaults to 0

matrix(#rest row-vectors) => <matrix> [Function]

Matrix will return a new matrix containing the given vectors as the rows of the matrix.

2. Functions

+ (x :: <matrix>, y :: <matrix>) => <matrix> [Method]
- (x :: <matrix>, y :: <matrix>) => <matrix> [Method]
* (x :: <matrix>, y :: <matrix>) => <matrix> [Method]
* (x :: <number>, y :: <matrix>) => <matrix> [Method]
* (x :: <matrix>, y :: <number>) => <matrix> [Method]

Basic arithmetic operations. The \* method on two matrices uses the algorithm from Sedgewick [1].

identity-matrix (#key dimensions :: <sequence>) => <matrix> [Function]

This returns a matrix filled with zeros, and having ones down the major diagonal. The following is an example:

augment-matrix (x :: <matrix>, y :: <matrix>) => <matrix> [Function]

This takes two matrices and returns a matrix that places the two arguments side by side in a single matrix. The following is an example:

gauss-jordan (x :: <matrix>) => <matrix> [Function]

This will take a matrix of dimension N by N+1, and return an N by 1 matrix. The result matrix is the solution to the system of equations represented by the argument matrix. For example, if your equations were

then the argument matrix would be

and gauss-jordan would return

representing x = 2 and y = 1. The algorithm for Gauss-Jordan was taken from Sedgewick [1].

inverse (x :: <matrix>) => <matrix> [Function]

Returns the inverse of the given matrix. For inverse to work, the matrix must be square, and this function signals an error if the argument matrix is not square. This function uses a modified Gauss-Jordon algorithm from Sedgewick [1] with quick error checking from Strang [2].

det (x :: <matrix>) => <matrix> [Function]

Returns the determinant of the given matrix. This function uses an algorithm from Strang [2].

transpose (x :: <matrix>) => <matrix> [Function]

Transposes the given matrix. Transpose takes each element, [i,j], and effectively stores it in location [j,i].

3. Future Revisions

Write functions for row-operations, eigen-value, and eigen-vector.

4. References

[1]: Sedgwick, Robert. Algorithms. 1993. Addison-Wesley Publishing Co.

[2]: Strang, Gilbert. Introduction to Linear Algebra. 1993. Wellesley-Cambridge Press.

Send comments and bug reports to gwydion-bugs@cs.cmu.edu