By Richard A. Reyment, K. G. Jvreskog

ISBN-10: 0511524889

ISBN-13: 9780511524882

ISBN-10: 0521412420

ISBN-13: 9780521412421

ISBN-10: 0521575567

ISBN-13: 9780521575560

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**Additional info for Applied Factor Analysis in the Natural Sciences**

**Sample text**

Null matrix A null matrix is a matrix all elements of which are zero. This matrix is the analog of zero in scalar algebra. 6 ELEMENTARY MATRIX ARITHMETIC Equality of matrices Two matrices are equal if all corresponding elements are equal. It follows that the matrices must be of the same order. Addition and subtraction of matrices As with vectors, the addition of two matrices is carried out by adding together corresponding elements of the matrices. The result is a matrix of the same order as the two matrices being summed.

In Fig. 1, we used only two coordinate axes, representing quartz and hornblende, respectively. 1. 1. 2. 1. 1, the objects can be thought of as vectors located in a three-dimensional space (Fig. 2). 1 would require four mutually perpendicular axes. This is naturally impossible in three-dimensional space and so, for the quadrivariate situation, we must think in terms of abstract space. The four elements of a row vector of observations give the coordinates of the object measured in four-dimensional space.

In Fig. 15C, the common order of the factors is r and r < s < t. If we find in this case that factors cannot be found of which the common order is less than r, then the rank of X is r. It follows from this that the rank of a matrix cannot exceed its smaller dimension; a data matrix, for example, must have a rank equal to, or less than, the number of columns or rows in it, whichever is the lesser. The rank of a product moment matrix derived from the data matrix cannot exceed the smallest dimension of the data matrix.

### Applied Factor Analysis in the Natural Sciences by Richard A. Reyment, K. G. Jvreskog

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