Vectors and Matrices
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Vectors and Matrices book
Vectors are presumed to be column vectors unless specified otherwise. The results of addition and subtraction of two vectors are vectors of the same order. The results of adding to, subtracting from or multiplying a vector by a scalar are vectors of the same order. Vectors cannot be multiplied together in a usual way but a useful scalar function of two vectors is the scalar product (or inner product). This chapter introduces some illustrations of uses of vectors and matrices in statistics. It begins with the basic formulation of linear models and multivariate analysis. In the context of a simple linear model, the variables are regarded as non-random or design variables and the matrix of observations as the design matrix in the sense that specific values of them can be chosen to take observations of one variable which depends upon them, the form of the dependence being a linear function plus some random error.