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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.
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Why transpose of a matrix is orthogonal?
It need not be, so the question makes no sense!
When are vectors orthogonal?
When they are at right angles to one another.
What is idempotent matrix?
An idempotent matrix is a matrix which gives the same matrix if we multiply with the same. in simple words,square of the matrix is equal to the same matrix. if M is our matrix,then MM=M. then M is a idempotent matrix.
What is a reduced matrix?
Reduced matrix is a matrix where the elements of the matrix is reduced by eliminating the elements in the row which its aim is to make an identity matrix.
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
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.
Why transpose of a matrix is orthogonal?
It need not be, so the question makes no sense!
How do you check orthogonality of a matrix using arrays?
the transpose of null space of A is equal to orthogonal complement of A
What does rotation mean in termsof inverse of orthogonal matrix?
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.
What do you understand by rotational and irrotational fields?
Irrotational fields are conservative, simply connected (path independent), and have no curl (del cross the field) = 0Rotational fields are orthogonal MTM=I, symmetrical, representable in any finite dimension through orthogonal matrix multiplication
What is the definition of orthogonal signal space?
Orthogonal signal space is defined as the set of orthogonal functions, which are complete. In orthogonal vector space any vector can be represented by orthogonal vectors provided they are complete.Thus, in similar manner any signal can be represented by a set of orthogonal functions which are complete.
Can the difference of 2 vectors be orthogonal?
The answer will depend on orthogonal to WHAT!
What is the orthogonal planning in ancient Greece?
it is planning of orthogonal planning
What is orthogonal planning in ancient Greece?
it is planning of orthogonal planning
When was Orthogonal - novel - created?
Orthogonal - novel - was created in 2011.
Self orthogonal trajectories?
a family of curves whose family of orthogonal trajectories is the same as the given family, is called self orthogonal trajectories.
