O'Reilly logo

Vectors, Pure and Applied by T. W. Körner

Stay ahead with the world's most comprehensive technology and business learning platform.

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, tutorials, and more.

Start Free Trial

No credit card required

3

The algebra of square matrices

3.1 The summation convention

In our first chapter we showed how a system of n linear equations in n unknowns could be written compactly as

images

In 1916, Einstein wrote to a friend (see, for example, [26])

I have made a great discovery in mathematics; I have suppressed the summation sign every time that the summation must be made over an index which occurs twice . . .

Although Einstein wrote with his tongue in his cheek, the Einstein summation convention has proved very useful. When we use the summation convention with i, j, . . . running from 1 to n, then we must observe the following rules.

     

(1) Whenever the ...

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, interactive tutorials, and more.

Start Free Trial

No credit card required