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
In 1916, Einstein wrote to a friend (see, for example, )
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 ...