The first element in a matrix denotes the number of columns in the matrix. This number must be in parentheses and on a line by itself. A Matrix with no such identifier will be treated as a vector (1 column or 1 row). A vector is identical to a data list and may be used interchangeably as either a data list or a matrix.
All matrix elements must be separated by semicolons.
Matrices names must contain at least one vertical bar (|).
The title of the Data Slate that contains the matrix must correspond to matrix variable name used in the problem statement. For example, the title of the Data Board containing matrix |Xm must be |Xm.
Matrix operations available are :
|Xm ' : Transformation (' is the single quotation mark)
|Xm^ -1 : Matrix Inversion.
|Xm^ d : Find Determinant
|Xm*a : Matrix multiplied by a scalar
|Xm*|Xn : Matrix Multiplication
|Xm•|Xn : Dot Product ( Dot • produced with OPTION 8 )
|Xm-|Xn : Matrix Subtraction
|Xm+|Xn : Matrix Addition
Be sure that the number of columns is properly specified and that the rows and columns are compatible with the operation being performed. Consult The PowerMath manual for details.
Warning:
Operations on non-numeric matrices may consume considerable memory.
Notes on Inversion:
PowerMath calculates the inversion of purely numeric matrices in a reasonable amount of time. Currently, however, PowerMath does not have the ability to create efficient inversions of most symbolic matrices.
Matrices larger than 3 by 3 which contain elements such as (2y+6), are likely to stretch the list and memory management capabilities of PowerMath. Matrices which appear small (4 by 4), may in fact explode into huge expressions during intermediate evaluations. The resulting inversion elements are quite unwieldy. Inversion of a 4 by 4 matrix takes between 45 minutes and 5 hours, depending upon its makeup.
Under these circumstances, the inversion of a matrix which contains symbolic expressions may be impractical because of the computation time required. To minimize these inconveniences, Inversion of matrices containing symbolic expressions has been limited to a size of 4 by 4.
More efficient algorithms for computing the inversion of a matrix, and for calculating the Greatest Common Divisor of complicated expressions, are subjects of future enhancements.
Note that an Error Message is displayed when the inversion matrix is a singular matrix. Matrices are singular if their determinant is zero.
