Correlation matrices (along with their unstandardized counterparts, covariance matrices) underlie the majority the statistical methods that researchers use today. A correlation matrix is more than a matrix filled with correlation coefficients. The value of one correlation in the matrix puts constraints on the values of the others, and the multivariate implications of this statement is a major theme of the volume. Alexandria Hadd and Joseph Lee Rodgers cover many features of correlations matrices including statistical hypothesis tests, their role in factor analysis and structural equation modeling, and graphical approaches. They illustrate the discussion with a wide range of lively examples including correlations between intelligence measured at different ages through adolescence; correlations between country characteristics such as public health expenditures, health life expectancy, and adult mortality; correlations between well-being and state-level vital statistics; correlations between the racial composition of cities and professional sports teams; and correlations between childbearing intentions and childbearing outcomes over the reproductive life course. This volume may be used effectively across a number of disciplines in both undergraduate and graduate statistics classrooms, and also in the research laboratory.

# The Mathematics of Correlation Matrices

### The Mathematics of Correlation Matrices

Numbers are basic mathematical elements. Most people have a good intuition for what a number is. Seven is a number, as is −182.1. π (the ratio of a circle’s circumference to its diameter, approximately 3.14159) is also a number. There are different types of numbers, such as integer, rational, irrational, and real numbers. Algebra and more advanced number theory textbooks can be consulted to develop understanding of numbers.

Numbers have characteristics. For example, a number can be whole or a decimal. A number can be positive or negative, real or imaginary. The number 2 is even; the number 7 is prime. Integer numbers are either even or odd. Even integer numbers bigger than 2 cannot be prime. Knowing the characteristics ...