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

By Richard A. Reyment, K. G. Jvreskog

Utilized multivariate statistics has grown right into a examine zone of just about limitless capability within the normal sciences. The tools brought during this ebook can effectively decrease plenty of information to conceivable and interpretable shape. The authors supply exact cognizance to tools of strong estimation and the id of abnormal and influential observations. This textbook goals to introduce scholars of the traditional sciences to the strong means of issue research and to supply them with the history essential to have the capacity to adopt analyses all alone. The authors clarify new strategies intimately, and supply mathematical history the place wanted.

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Example text

Diagonal matrices A diagonal matrix is a square symmetrical matrix, the off-diagonal elements of which are all zero. 6 Elementary matrix arithmetic 27 the identity matrix, which has ones in the principal diagonal. The identity matrix serves the same function in linear algebra as the number 1 in scalar arithmetic. 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.

A unit column vector is denoted by 1. The order of a unit vector may be deduced from the context in which it is used. The null vector is a vector all the elements of which are 0. 5) (4,2) I 2. 3. 5. 4. 5]. 2 . 4 THE GEOMETRY OF VECTORS Some vector operations can be given a geometrical interpretation, which is often useful in understanding factor analysis. We illustrate our examples for two dimensions, but the relations hold for any number of dimensions. Resultant vector The vector representing the sum of two other vectors gives the coordinates of the resultant vector.

To form the product C = AB, assuming the orders compatible, every element of C is equal to the minor product of the corresponding row vector of A and the column vector of B. We shall now demonstrate the truth of these statements by recourse to a worked example. Consider the matrices A- J and B = 1 2 3 4 2 1 Since A is 2 by 3 and B is 3 by 2, a product can be formed. 6 Elementary matrix arithmetic 29 C = AB, the element cu is made from the minor product of the first row vector of A and the first column vector of B: c n = 2 x 1 + 3 x 2 + 1 x 3 = 11.

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