(a) Calculate QW and WQ. (b) Compute [Q, W]. (c) Compute trQ, trW, and tr[Q, W]....

   

  

 

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(a) Calculate QW and WQ. (b) Compute [Q, W]. (c) Compute trQ, trW, and tr[Q, W]. (d) Calculate det Q and det W. (e) Calculate the inverse Q-¹. Simplify the result so that no complex numbers are in the denominators or appear as overall factors. [Hint: you should find that (Q-¹)12 = (−9 – 3i) /10.] (f) There is a matrix operation called the HERMITIAN CONJUGATE which is the complex conjugate of every entry of the matrix combined with the transpose of the matrix: M (MT)* (that's the same as (M*)T. Compute Q¹. = (g) Compute QtQ. Then compute det(Q¹Q). (h) A square matrix M with the property that M¹ = M is called a HERMITIAN MATRIX. Is Q Hermitian? Is Q¹Q? = 1 - 2i 0 3i −1+i and i 1 i = (₁ + + ²+4) 3+i 0 W = (a) Calculate QW and WQ. (b) Compute [Q, W]. (c) Compute trQ, trW, and tr[Q, W]. (d) Calculate det Q and det W. (e) Calculate the inverse Q-¹. Simplify the result so that no complex numbers are in the denominators or appear as overall factors. [Hint: you should find that (Q-¹)12 = (−9 – 3i) /10.] (f) There is a matrix operation called the HERMITIAN CONJUGATE which is the complex conjugate of every entry of the matrix combined with the transpose of the matrix: M (MT)* (that's the same as (M*)T. Compute Q¹. = (g) Compute QtQ. Then compute det(Q¹Q). (h) A square matrix M with the property that M¹ = M is called a HERMITIAN MATRIX. Is Q Hermitian? Is Q¹Q? = 1 - 2i 0 3i −1+i and i 1 i = (₁ + + ²+4) 3+i 0 W =

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To calculate the matrix products and traces as requested we first need to define the matrices Q and W Q 12i 3i 0 1i W i 1i 3i 0 1 Calculate QW Q multi... View the full answer