orthogonal

How do you prove the determinant of an orthogonal matrix is +/- 1?
Q. In Linear Algebra, an orthogonal matrix is composed of rows and columns that are orthonormal vectors. How do you construct a proof that proves the determinant of an orthogonal matrix is +/- 1?
Asked by linus108nicole - Thu May 27 14:13:04 2010 - - 1 Answers - 0 Comments

A. Let "A" be an orthogonal matrix. Then by definition of an orthogonal matrix, the transpose of A is equal to the inverse of A: A^T = A^(-1) Then remember what the definition of an inverse matrix is: A*A^(-1) = I "I" will be the identity matrix. Now you can substitute in A^(T) for A^(-1) since A^(T) = A^(-1): A*A^(T) = I Take the determinant of both sides: det(A*A^(T)) = det(I) Remember that the det(I) is always 1: det(A*A^(T)) = 1 Then you should also remember a theorem det(A*B) = det(A) * det(B): det(A) * det(A^(T)) = 1 And finally there's one more theorem you need to know: that det(A) = det(A^T): det(A) * det(A) = 1 Simplify: (det(A)) = 1 And you get: det(A) = 1
Answered by Markus0003000 - Thu May 27 14:35:18 2010

Could it be possible that the physical universe is orthogonal to the spiritual realm?
Q. Just some weird thoughts i would like to share with anyone out there who may have some ideas- could it be that the physical and spiritual universes are orthogonal to one another, and that from an observer looking in at us from the outside, both realms appear to be two dimensional? could there be (random) areas which connect the two universes, ocassionally making it possible to have so-called "paranormal" experiences? thanks guys- you're great!
Asked by fermion_gas - Sat Apr 21 17:35:51 2007 - - 4 Answers - 0 Comments

A. Actually there is some evidence that the situation you describe is false. If the people in this other dimension can "see" us, this means that photons are leaving our universe and travelling to theirs. We would notice that sometimes energy is disappearing in physics experiments or that electric forces do not drop off exactly like the radius squared. This has been measured very carefully for electrical forces. In contrast to electricity, gravitational forces have not been tested at small distances (less than a millimeter or so) so the existence of parallel universes that are very close to us and with which we can only communicate through gravitational forces has not been ruled out. This might not be the kind of spiritual realm you are… [cont.]
Answered by b_physics_guy - Sun Apr 22 05:22:46 2007

How do I draw by hand a 3d representation of an object based on orthogonal views (ie front,left,top) of it.?
Q. I remember doing this in college but I can't for the life of me remember. It was some sort of draft/mechanical drawing class. We had three orthogonal views in 3 quadrants of a grid, and in the fourth we used the other three to create a "3D" drawing of the object.
Asked by Karl K - Thu Mar 19 13:04:06 2009 - - 2 Answers - 0 Comments

A. Do you remember isometric drawings? That is the simpliest way to do it by hand. Here is one of several references on the subject: Except for piping spool drawings, Isometric drawings are typically drawn to scale.
Answered by oil field trash - Thu Mar 19 15:45:07 2009