inear lgebra and unctional nalysis the purpose of this appendix is to review some important topics in linear algebra and functional analysis we assume that the reader has some familiarity with matrix and vector operationsincluding matrix multiplication and the computation of determinants vector spacesbasesand matrices linear algebra is the study of vector spaces and linear mappings vectors areby definitionelements of some vector space and satisfy the usual rules of addition and scalar multiplicatione vector space if and vthen ax by for all ab (or cwe will be dealing mostly with vectors in the euclidean vector space rn for some that iswe view the points of rn as objects that can be added up and multiplied with scalare ( ( ( for points in sometimes it is convenient to work with the complex vector space cn instead of rn see also section vectors vk are called linearly independent if none of them can be expressed as linear combination of the othersthat isif an vn then it must hold that ai for all linearly independent definition basis of vector space set of vectors { vn is called basis of the vector space if every vector can be written as unique linear combination of the vectors in bbasis an vn the (possibly infinitenumber is called the dimension of dimension