SPSS® 12.0 Command Syntax Reference

Example
Overview
MATRIX—END MATRIX 915
MATRIX.
READ A /FILE=MATRDATA /SIZE={6,6} /FIELD=1 TO 60.
CALL EIGEN(A,EIGENVEC,EIGENVAL).
LOOP J=1 TO NROW(EIGENVAL).
+ DO IF (EIGENVAL(J) > 1.0).
+ PRINT EIGENVAL(J) / TITLE="Eigenvalue:" /SPACE=3.
+ PRINT T(EIGENVEC(:,J)) / TITLE="Eigenvector:" /SPACE=1.
+ END IF.
END LOOP.
END MATRIX.
The MATRIX and END MATRIX commands enclose statements that are executed by the SPSS
matrix processor. Using matrix programs, you can write your own statistical routines in the
compact language of matrix algebra. Matrix programs can include mathematical calculations,
control structures, display of results, and reading and writing matrices as character files
or SPSS data files.
As discussed below, a matrix program is for the most part independent of the rest of the
SPSS session, although it can read and write SPSS data files, including the working data file.
This section does not attempt to explain the rules of matrix algebra. Many textbooks, such
as Hadley (1961) and O’Nan (1971), teach the application of matrix methods to statistics.
The SPSS MATRIX procedure was originally developed at the Madison Academic
Computing Center, University of Wisconsin.
Terminology
A variable within a matrix program represents a matrix, which is simply a set of values
arranged in a rectangular array of rows and columns.
• An n× m (read “n by m”) matrix is one that has n rows and m columns. The integers n and
m are the dimensions of the matrix. An n × m matrix contains n× m elements, or data
values.
• An n × 1 matrix is sometimes called a column vector, and a 1 × n matrix is sometimes
called a row vector. A vector is a special case of a matrix.
• A 1× 1 matrix, containing a single data value, is often called a scalar. A scalar is also a
special case of a matrix.
• An index to a matrix or vector is an integer that identifies a specific row or column. Indexes
normally appear in printed works as subscripts, as in A31, but are specified in the matrix
language within parentheses, as in A( 3,1)
. The row index for a matrix precedes the column
index.
• The main diagonal of a matrix consists of the elements whose row index equals their
column index. It begins at the top left corner of the matrix; in a square matrix, it runs to the
bottom right corner.
• The transpose of a matrix is the matrix with rows and columns interchanged. The transpose
of an n × m matrix is an m× n matrix.