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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.
