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What is a non-singuar matrix?
A non-singular matrix is basically one that has a multiplicative inverse. More specifically, a matrix "A" is non-singular if there is a matrix "B", such that AB = BA = 1, where "1" is the unity matrix. Non-singular matrixes are those that have a non-zero determinant. Singular and non-singular matrixes are only defined for square matrixes.
How do you check orthogonality of a matrix using arrays?
the transpose of null space of A is equal to orthogonal complement of A
Is a singular matrix an indempotent matrix?
A singular matrix is a matrix that is not invertible. If a matrix is not invertible, then:• The determinant of the matrix is 0.• Any matrix multiplied by that matrix doesn't give the identity matrix.There are a lot of examples in which a singular matrix is an idempotent matrix. For instance:M =[1 1][0 0]Take the product of two M's to get the same M, the given!M x M = MSo yes, SOME singular matrices are idempotent matrices! How? Let's take a 2 by 2 identity matrix for instance.I =[1 0][0 1]I x I = I obviously.Then, that nonsingular matrix is also idempotent!Hope this helps!
Why singular matrix should have non zero vector?
There is no reason why it should! So the question is based on an incorrect assumption. A matrix of only zero vectors will be singular!
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.
