Best Answer

The inverse of a rotation matrix represents a rotation in the opposite direction, by the same angle, about the same axis.

Since M-1M = I, M-1(Mv) = v. Thus, any matrix inverse will "undo" the transformation of the original matrix.

User Avatar

Wiki User

11y ago
This answer is:
User Avatar

Add your answer:

Earn +20 pts
Q: What does rotation mean in termsof inverse of orthogonal matrix?
Write your answer...
Still have questions?
magnify glass
Related questions

What is an orthogonal matrix?

A matrix A is orthogonal if itstranspose is equal to it inverse. So AT is the transpose of A and A-1 is the inverse. We have AT=A-1 So we have : AAT= I, the identity matrix Since it is MUCH easier to find a transpose than an inverse, these matrices are easy to compute with. Furthermore, rotation matrices are orthogonal. The inverse of an orthogonal matrix is also orthogonal which can be easily proved directly from the definition.

If A is an orthogonal matrix then why is it's inverse also orthogonal?

First let's be clear on the definitions.A matrix M is orthogonal if MT=M-1Or multiply both sides by M and you have1) M MT=Ior2) MTM=IWhere I is the identity matrix.So our definition tells us a matrix is orthogonal if its transpose equals its inverse or if the product ( left or right) of the the matrix and its transpose is the identity.Now we want to show why the inverse of an orthogonal matrix is also orthogonal.Let A be orthogonal. We are assuming it is square since it has an inverse.Now we want to show that A-1 is orthogonal.We need to show that the inverse is equal to the transpose.Since A is orthogonal, A=ATLet's multiply both sides by A-1A-1 A= A-1 ATOr A-1 AT =ICompare this to the definition above in 1) (M MT=I)do you see how A-1 now fits the definition of orthogonal?Or course we could have multiplied on the left and then we would have arrived at 2) above.

What is leontief inverse matrix?

(I-A)-1 is the Leontief inverse matrix of matrix A (nxn; non-singular).

Is Inverse of the inverse matrix the original matrix?

Let A by an nxn non-singular matrix, then A-1 is the inverse of A. Now (A-1 )-1 =A So the answer is yes.

How are the inverse matrix and identity matrix related?

If an identity matrix is the answer to a problem under matrix multiplication, then each of the two matrices is an inverse matrix of the other.

Verify that H is an elementary orthogonal matrix.Where H is householder matrix?

For the matrix , verify that

Define inverse of matrix?

From Wolfram MathWorld: The inverse of a square matrix A, sometimes called a reciprocal matrix, is a matrix A-1 such that AA-1=I where I is the identity matrix.

Does every square matrix have an inverse?

No. A square matrix has an inverse if and only if its determinant is nonzero.

What are the applications of det of a matrix?

it is used to find the inverse of the matrix. inverse(A)= (adj A)/ mod det A

How do you find a variable in a matrix if there is no inverse?

The fact that the matrix does not have an inverse does not necessarily mean that none of the variables can be found.

Why transpose of a matrix is orthogonal?

It need not be, so the question makes no sense!

How do you call a matrix that if you multiplied it by the original matrix you would get the identity matrix?

That is called an inverse matrix