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Is idempotent matrix a square matrix?
A square matrix K is said to be idempotent if K2=K.So yes K is a square matrix
What is the determinant of an idempotent matrix?
0 or 1
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!
Example for idempotent matrix?
1 0 0 0 1 0 0 0 1
How do you prove idempotent law?
The same way you prove anything else. You need to be clear on what you have and what you want. You can prove it directly, by contradiction, or by induction. If you have an object which is idempotent (x = xx), you will need to use whatever definitions and theorems which apply to that object, according to what set it belongs to.
