Transcription of Introduction to Matrix Algebra - Statpower
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Introduction to Matrix Algebra - Statpower
4 Introduction to MatrixAlgebraIn the previous chapter, we learned the algebraic results that form the founda-tion for the study of factor analysis and structural equation modeling. Theseresults, powerful as they are, are somewhat cumbersome to apply in morecomplicated systems involving large numbers of variables. Matrix algebraprovides us with a new mathematical notation that is ideally suited for de-veloping results involving linear combinations and transformations. Once wehave developed a few basic results and learned how to use them, we will beready to derive the fundamental equations of factor analysis and BASIC TERMINOLOGYD efinition ( Matrix )Amatrixis defined as an ordered array of numbers, ofdimensionsp, standard notation for a matrixAof orderp,qwill be:pAqThere are numerous other notations. For example, one might indicate amatrix of orderp,qasA(p q).
56 INTRODUCTION TO MATRIX ALGEBRA 6. A scalar matrix 200 020 002 7. A symmetric matrix 123 224 342 4.1.2 Partitioning of Matrices In many theoretical discussions of matrices, it will be useful to conceive of a
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