# Recent content by jiles-smith

1. ### Quantum Mechanics Entangled States

Your definition of entanglement is a bit off. A state is entangled if it cannot be written in terms of a product of two (or more if your looking at many qubits) single qubit states. i.e. if Alice and Bob share two qubits in a general state: \vert\psi_{AB}\rangle=a\vert 00\rangle+b\vert...
2. ### Characteristic and Minimal polynomials of matrices

Homework Statement Let V=C^4 and consider the linear map V->V given by the matrix: {{12,-6,6,-6},{2,21,21,51},{-3,12,12,30},{1,-9,-9,-21}} (Each {...} denotes a row, tried to use Latex but got extremely confused!) Given that chA(X)=(X-6)^4, calculate: (i) The power such that...
3. ### Linear maps: finding matrix

well i have just changed direction a bit but here is what i have so: T(1,0,0)=(0,1,0,0); T(0,1,0)=(0,0,1,0); T(0,0,1)=(0,0,0,1) So the matrix would be: ((0,0,0),(1,0,0),(0,1,0),(0,0,1)) (Each sub-bracket is a row)
4. ### Linear maps: finding matrix

okay, so i have used the basis for R^3 and got a diagonal matrix with the elements x. Given the equation T(P(x))=x P(x) it looks like it could work. Is this correct? cheers
5. ### Linear maps: finding matrix

so would the basis in R^2 in vector form be: {1,0,0},{0,1,0},{0,0,1}? If so, how would you get this in terms of the R^3 basis?
6. ### Linear maps: finding matrix

Homework Statement Let T:R[x]2->R[x]3 be defined by T(P(x))=xP(x). Compute the matrix of T with respect to bases {1,x,x^2} and {1,x,x^2,x^3}. Find the kernel and image of T. The Attempt at a Solution I genuinely have no idea where to start on this, any pointers you can give me would be...