LINEAR ALGEBRA BY PAVEL GRINFELD

 A second look towards the subject through a tremendous collection of excercises and solutons.

LINEAR ALGEBRA  by PAVEL GRINFELD,

is a mathematical book, that contains various topics and their solutons. Linear algebra is  widy informated book, that contains a lot of mathematical knowlede in algebric branch.

DESCRIPTION;

Linear algebra is a grand subject. Because it is fundamentally different from any high school mathematics, and because of the wildly varying quality of instructors, not all students enjoy learning it.

If you hated it, I blame the instructor. There I said it. In either case,whether you loved it or hated it, it takes several passes to learn

linear algebra to the point that it becomes one of your favorite tools,one of your favorite ways of thinking about practical problems.

This little textbook invites you on your second pass at linear algebra. Of course, your second pass may take place alongside your

first pass. You may find this textbook particularly useful if you are studying for a test. Our goal is to take a step back from the mechanics of the subject with an eye towards gaining a larger view.

A larger view, however, is achieved in small steps. We are not hoping for a big revelation but for a few small aha! moments. It simply takes time to put together the grand puzzle of linear algebra.

You will get there, and the point, as the cliche goes, is to enjoy the ride.

Psychology in mathematics is everything. I chose the topics according to the impact I feel they would make on your relationship with linear algebra. The textbook's utmost goal is to make you feel

positively about the subject. You will find that some topics are surprisingly simple, others surprisingly tough. Some topics have important applications, others have none at all. Some were well presented in your linear algebra course, others skipped altogether.

However, I hope you will find that all topics bring you a little closer to the subject of linear algebra.

APPLICATIONS;

1;The applications of linear algebra are extraordinarily broad.

The subject applies to any type of objects that can be added together and multiplied by numbers. These objects are united by the term vector and include pointed segments, polygons or – more

generally – functions, sets of numbers organized in a column,matrices, currents, voltages, substances in chemical reactions,strains and stresses in elastic bodies, sound signals, portfolios of

financial securities.

2; Linear algebra studies the commonalities among these

objects. However, focusing on the commonalities is

counterproductive if one ignores the differences. It is that the fact that these objects are all uniquely different that makes linear algebra

such a remarkable tool. We therefore invite the reader to accept and treat each object on its own terms. If the problem relates to pointed

segments which we call geometric vectors, by all means let us have a geometric discussion and talk about straight lines, lengths, and

angles. Do not rush to associate a geometric vector in the plane with a pair of numbers.

3;There seems to be a lamentable tradition to refer the space of our everyday physical experience to Cartesian coordinates, whether or not it is the best

coordinate system and, even more lamentably, whether or not coordinates are needed in the first place. If I may speak for Descartes, he would have been appalled by this state of affairs! His

ingenious invention of coordinates was meant to unite the worlds of algebra and geometry. The knee-jerk reaction to translate a physical problem to numbers, typically by introducing a Cartesian coordinate systems, and often doing so tacitly, usually leads to loss of simplicity, vision, clarity, and understanding.

PROS;

easy to read

Cons;

Need further explanations about solutions.

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