While linear algebra is, strictly speaking, a subject of algebra and not of analysis or

diﬀerential equations (which are, along with probability theory, the basic mathematical

tools used for studying quantitative ﬁnance), the theory of vector spaces is so fundamen-

tal to the modern formulation of either, that it is necessary to study it before proceeding

too far. Indeed, the theory has proven itself to be perhaps the most inﬂuential in unifying

signiﬁcant branches of modern mathematics