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# definition of an orthogonal matrix watch

1. so..... is this right?

An orthogonal matrix is one where when 2 of any of the columns are multiplied together they equal zero.

eg.

a b c
d e f
g h i

is orthogonal when

a
d
g

multiplied by

b
e
h

equals zero
2. You also need that

a
d
g

multiplied by

a
d
g

equals 1, etc.

You can put all the conditions for orthogonality together as M M^T = I.
3. A matrix is orthogonal if it's transpose equals its inverse, i.e. . This follows from the fact that the (dot) products of all pairs of its column vectors are zero, which in turn follows from the fact that its column vectors are normalized.

In other words, it's not just if two columns multiplied by each other equal zero - it's:
(a, d, g) . (b, e, h) = 0
(a, d, g) . (c, f, i) = 0
(b, e, h) . (c, f, i) = 0
4. so transposing the matrix and multiplying the matrix by its transpose gets I
5. thanks dvs - i think i get it now - at least, i get it better than i did 10 minutes ago...

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