Determining the equation for a matrix and confirming the inverse, eigenvalues
Details:
I have think the answer to question (a) is theta^2 [(1-p)I + pJ]. But when I am multiplying the sigma and the sigma inverse I still have "stuff" at the tail end of the identity......being added. I know I should be left with the identity if the two pieces are the inverses to each other.

... associated with are: (1.9) Note that the diagonalizing matrix is (we already know the eigenvector associated with eigenvalue ): (1.10) Its inverse is: (1.11 ...

... its eigenspaces is equal to n. Since matrices and linear ... of A, with xi being an eigenvector corresponding to ... This will give a diagonal matrix, say D, with the ...

... the eigenvalues and their associated eigenvectors are: (1.5 ... Since D is a diagonal matrix, we get ... homogeneous first order differential equations using matrices. ...

Linear Transformations, Matrices, Orthogonal Projections. ... (b) Find the eigenvalues and corresponding eigenvectors of A. (c ... (d) Find an invertible matrix Q such ...

... Deduce that the set H consisting of matrices of the ... that V has a basis consisting of eigenvectors of f ... a basis with respect to which the matrix representing f ...

... of sj where sj is the Pauli matrix in the ... In this basis, the Pauli matrices representing the spins are ... as well, it is imperative to find the eigenvectors of sy ...

... 2. The system is: (2.1) When we write it in matrix form we get: (2.2) The eigenvalues are: (2.3) The first eigenvector is: (2.4) The second eigenvalue is: ...

... this won't work for 4 by 4 matrices and higher ... linearly independent vectors, each of which is an eigenvector of A ... the same steps using a general n by n matrix). ...

... 2 ≈ 0.4142 and its corresponding 2 eigenvector is X ... 1 A = I Where I is obviously the identity matrix. ... recommended even when 3×3 matrices are concerned ...