Template talk:High School Mathematics Extensions/Matrices

The multiplication section is unclear... r3m0t (cont) (talk) 10:07, 27 Mar 2004 (UTC)

What is &delta;? r3m0t (cont) (talk) 10:00, 15 Apr 2004 (UTC)


 * The Kronecker delta. The definition there is what the function is, however, and that's about it... Dysprosia 10:09, 15 Apr 2004 (UTC)
 * It's the Greek letter, delta.


 * Considering I wrote &amp;delta; in the source code, I already knew that ;) r3m0t (cont) (talk) 11:09, 16 Apr 2004 (UTC)

If a variable is a matrix, is it always capitalised? Is it always italicised? r3m0t (cont) (talk) 11:36, 15 Apr 2004 (UTC)


 * When you write on paper, capitalize it. When it's printed, I think convention is to have capitals, bold, but not italicize. Dysprosia 12:15, 15 Apr 2004 (UTC)

I thought that one of the important things about multiplication is that it is commutative i.e. $$ab = ba$$ but it seems that with matrices this is not so. Why is this definition of multiplying matrices more useful than an alternative, commutative one? r3m0t (cont) (talk) 11:43, 15 Apr 2004 (UTC)


 * No, matrix multiplication is noncommutative. AB != BA. It stems from the definition of matrices representing systems of equations, and is a bit complex to quickly explain here. If you like, pick two matrices, multiply them in the "two-finger" method (not sure if this nifty method is explained here), and then change the order. You might not get the same answer. Dysprosia 12:15, 15 Apr 2004 (UTC)


 * As for why we use that definition, being noncommutative is very useful. It happens a lot in real problems. E.g rotate a book 90 degrees round a vertical axis then 90 degrees round an horizontal axis and it'll end up differently orientated to if you spin it roun the horizontal axis before the vertical. When you rotate things, order matters, so rotation is not commutative. We need non-commutating matrices to describe it, and many other physically interesting systems. Carandol


 * Or that a matrix represents a linear transformation, and that performing one transform before another is not necessarily the same as doing it in the other order. Dysprosia 12:39, 15 Apr 2004 (UTC)

problem with exercises
I have found a problem with exercise 4 in the exercises section after the text about multiplication of diagonal matrices. It seems to me that the multiplication of the two matrices should be reversed eg instead of c*b what is is now, it should be b*c. Otherwise this equation isn't usefull for the e and f part of the exercise.

The A defined in the equation in the d part of the exercise isn't the same A as defined in the a part of the exercise, as you can see below:

\begin{pmatrix} 3&1\\ 1&1\\ \end{pmatrix} \begin{pmatrix} 3&0\\ 0&1\\ \end{pmatrix} \begin{pmatrix} \frac{1}{2}&-\frac{1}{2}\\ -\frac{1}{2}&\frac{3}{2}\\ \end{pmatrix} = \begin{pmatrix} 4&-3\\ 1&0\\ \end{pmatrix} $$ Mmartin 21:33, 13 Aug 2004 (UTC)


 * My mistake, thanks for pointing it out. It's been fixed Xiaodai 14:25, 14 Aug 2004 (UTC)

Update to consistency
Need to change the vectors to have arrows on them, just to be consistency. This is a reminder that i should do that. Xiaodai 12:48, 30 Jan 2005 (UTC)

Cofactor Expansion
Shouldn't you talk about cofactor expansion for finding the determinant of a matrix? Giving only the formula for a 2x2 matrix won't take readers very far. At the very least, give them the general method to find determinants using permutations.