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Determinant of Orthogonal 
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#1
Dec1007, 07:08 PM

P: 303

Hi I had a final today and one of the questions was
find all the possible values of det Q if Q is a orthogonal matrix I m still wondering how would I do this? Any ideas? 


#3
Dec1007, 07:55 PM

P: 303

well i guess the vectors which make up the matrix are orthogonal and so have a dot product of 0?
and the transpose of an orthogonal matrix is its inverse but im not sure how to use this to find out all values of the determinant 


#4
Dec1007, 08:01 PM

Mentor
P: 8,316

Determinant of Orthogonal
Ok, so you know the transpose of an orthogonal matrix is its inverse. So, we have [itex]M^TM=I[/itex]. Now, let's take the determinant of this; [itex]det(M^TM)=det(I)[/itex]. I presume you know what the right hand side is equal to. Now, what can one say about the relationship between the determinant of a matrix, and the determinant of its transpose?



#5
Dec1507, 07:53 PM

P: 303

but how is the determinant of(M^TM) = det(M)
if M is a orthogonal matrix by the way since you said det (i) its 1..right? and I do know the det(M^t) = det (M) but det (M^tM) = 1 and im not understanding how that is = det (M) 


#6
Dec1507, 07:55 PM

Mentor
P: 8,316




#7
Dec1507, 08:06 PM

HW Helper
P: 860

hmmm...salman213 perhaps this is the theorem you want
det(AB) = det(A)det(B) 


#8
Dec1607, 03:09 PM

P: 303

oh okk..cool..thanks



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