PrefaceIs Linear Algebra part of Modern Algebra or is it baby Functional Analysis? It dependssomewhat on your interests. I tend to lean toward the baby functional analysis, but algebraicideas are certainly important and some would give strong arguments that these ideas are ofmost significance. Certainly it is all about linear transformations however you look at it,and the canonical forms are completely algebraic in nature. I have therefore, chosen topresent the subject in two parts, the first being Linear Algebra as a part of Algebra withvery little if any reference to Analysis. It involves general fields of scalars and makes noreference or minimal reference to completeness. This is all about polynomials as formalobjects and the division algorithm. After this, the more analytical aspects of this subject areconsidered, inner products, numerical methods, applications to differential equations andso forth. The field of scalars will be the real or complex numbers. Some analysis ideas doin fact creep in to the first part, but they are generally fairly rudimentary, occur as examples,and will have been seen in calculus. This book is not meant to be read before a calculuscourse.

It may be that increased understanding is obtained by this kind of presentation in whichthat which is purely algebraic is presented first. This also involves emphasizing the mini-mum polynomial more than the characteristic polynomial and postponing the determinant.In each part, I have included a few related topics which are similar to ideas found in linearalgebra or which have linear algebra as a fundamental part.

The book is a re written version of an earlier book. It also includes several topics not inthis other book. I have tried to introduce rings and modules in the context of a presentationof the canonical forms.

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