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The trace of a Hermitian matrix is real, because the elements on the diagonal are real. The trace of a permutation matrix is the number of fixed points of the corresponding permutation, because the diagonal term a ii is 1 if the i th point is fixed and 0 otherwise. The trace of a projection matrix is the dimension of the target space.
A framed trace diagram is a trace diagram together with a partition of the degree-1 vertices V 1 into two disjoint ordered collections called the inputs and the outputs. The "graph" underlying a trace diagram may have the following special features, which are not always included in the standard definition of a graph:
The trace of a rotation matrix is equal to the sum of its eigenvalues. For n = 2, a rotation by angle θ has trace 2 cos θ. For n = 3, a rotation around any axis by angle θ has trace 1 + 2 cos θ. For n = 4, and the trace is 2(cos θ + cos φ), which becomes 4 cos θ for an isoclinic rotation.
str(T) = the ordinary trace of T 00 − the ordinary trace of T 11. Let us show that the supertrace does not depend on a basis. Suppose e 1, ..., e p are the even basis vectors and e p+1, ..., e p+q are the odd basis vectors. Then, the components of T, which are elements of A, are defined as
Save a physical copy of important emails you've sent or received. Check out how to print emails and attachments in AOL Mail. 1. Open the email you'd like to print. 2. Click the Print icon. - A window will appear with your message. 2. Click the Print icon again. 3. Follow the browser prompts to finish printing.
The form comes with two worksheets, one to calculate exemptions, and another to calculate the effects of other income (second job, spouse's job). The bottom number in each worksheet is used to fill out two if the lines in the main W4 form. The main form is filed with the employer, and the worksheets are discarded or held by the employee.