Essays In Linear Algebra Gilbert Strang Pdf To Word

Editorial Reviews

Review

'... this delightful book is a most welcome addition to the library of any mathematician with an interest in applied linear analysis.' Vicentiu D. Radulescu, Zentralblatt MATH

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Book Description

Expository papers by a renowned mathematician and educator on the theory and applications of linear algebra, with video lectures on http://ocw.mit.edu. This text will be useful to students and researchers across all numerate disciplines and the author's commentary will appeal to those interested in mathematics as a human endeavour.

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Editorial Reviews

Review

'... this delightful book is a most welcome addition to the library of any mathematician with an interest in applied linear analysis.' Vicentiu D. Radulescu, Zentralblatt MATH

Read more

Book Description

Expository papers by a renowned mathematician and educator on the theory and applications of linear algebra, with video lectures on http://ocw.mit.edu. This text will be useful to students and researchers across all numerate disciplines and the author's commentary will appeal to those interested in mathematics as a human endeavour.

Read more

See all Editorial Reviews

NO_CONTENT_IN_FEATURE

NO_CONTENT_IN_FEATURE

Editorial Reviews

Review

'... this delightful book is a most welcome addition to the library of any mathematician with an interest in applied linear analysis.' Vicentiu D. Radulescu, Zentralblatt MATH

Read more

Book Description

Expository papers by a renowned mathematician and educator on the theory and applications of linear algebra, with video lectures on http://ocw.mit.edu. This text will be useful to students and researchers across all numerate disciplines and the author's commentary will appeal to those interested in mathematics as a human endeavour.

Read more

See all Editorial Reviews

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>I'm amazed that you say that calculus has had a much greater impact on society when virtually every database, graphics manipulation or economic analysis uses principles of linear algebra.

I'm not. Consider all of physics. Physics is written down in terms of differential equations. You need calculus to get these equations. In terms of graphics, for example, are you magically creating only static images that never change in time? How do you think people came up with the algorithms to do things like refraction or reflection? These all involve calculus. Calculus is the most important tool in applying mathematics to the real world. It is how we derive the models for pretty much everything I can think of. Any time you want to model something where anything changes, that is calculus. Any time you want to find an optimal solutions, that is calculus. I can't think of a single area of applied mathematics that doesn't use calculus in some form. Even mathematics in general, calculus is used in some form pretty much everywhere in some form, except maybe in the foundations of mathematics like set theory or logic.

Solving them, on the other hand, is a different problem. This is where linear algebra is important. When solving an ODE or PDE, when I discretise it, all I am doing is re-writing it as a giant linear algebra problem. Quantum mechanics, for example, is dedicated to finding the eigenvalues and eigenvectors of the Hamiltonian. Linear algebra provides the tools to solve the problems posed by calculus. But it isn't always required.

In fact, if you look at the history of linear algebra, it only really became wide-spread when quantum mechanics was developing since there is a deep connection between linear algebra and quantum mechanics. Heisenberg had never heard of a matrix before despite discovering Heisenberg matrix mechanics. He was told by Max Born that what he had been doing is actually this thing mathematicians called "matrices". Now linear algebra is a required course for physicists (incidentally, linear algebra was the first lecture I ever attended at university).

So I would argue that learning calculus is the most important thing someone should know mathematically, since it is the tool we use to build models. The second most is linear algebra since it provides us the tools to solve these problems. But in my mind, knowing how to derive these models is a lot more important than being able to solve them. That and linear algebra doesn't give you any insight into why we are solving the problem that way, it is just a tool to solve the problem.

Also in Calculus 1,2,3 and so on, you learn increasingly more complicated techniques of calculus to solve more problems. But when you start numerically solving them, linear algebra doesn't care. It doesn't care if your equation came from the Einstein field equations or Newton's second law. It's all the same to it. So in a sense, I can teach you everything you'll need to know about linear algebra in a single course but the same is not true of calculus, which requires multiple courses.

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