A Course on Statistics for Finance

Appendix A

Vectors and Matrices

This appendix is mainly a listing of background results that can be used for deeper understanding of the text material. There is a brief discussion and proof at times. Some of the results discussed here were presented also earlier in the text where needed.

A.1 Introduction

This appendix deals with arrays. A two-dimensional array is a matrix. An m× n (read “m -by-n”) matrix may be written as having m rows and n columns, the rows being horizontal lines, the columns being vertical lines.

Each line of a matrix is a vector. An m × 1 array is a column vector. A 1 × n array is a row vector.

A vector v with elements v1, v2,..., vm, say, may be pictured as a one-dimensional array, but its essence is that it is a function ...