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In the book "A First Course in General Relativity" by Schutz (1985 Edition) in chapter 2 there is a problem concerning summation that has me confused.

Note: This is not homework, just an interest of mine.

The given quantities are:

A = (5,0,-1,-6)

B = (0,-2,4,0)

C = [ 1 0 2 3

5 -2 -2 0

4 5 2 -2

-1 -2 -2 0 ]

Find:

A (super alpha) * C (sub alpha, beta); for all beta.

As usual, I apologize for not using LaTex but I can never get it to work right.

My attempt.

The only sum is on alpha because it is the only repeated upper and lower index. I should end up with a set of 4 numbers.

I followed the example given on page 41 of the book and applied it to this problem, but I got all 4 numbers wrong.

For the first value I calculated:

(1)*(5) + (0)*(0) + (2)*(-1) + (3)*(-6) = -15

The answer is given as (7, 1, 26, 17).

Any help on what I am doing wrong would be greatly appreciated.

Thanks

Matt

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# Schutz - A First Course in GR - Simple Summation Question

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