 Forum index » Science and Technology » Math
Author Message
aline
science forum beginner

Joined: 29 Nov 2006
Posts: 2 Posted: Wed Nov 29, 2006 2:37 am    Post subject: Linear operator and determinant Hi, I am having trouble with the following exercise.

1-Let V be the vector space of all nxn matrices over the field of
complex numbers, and let B be a fixed nxn matrix over C. Define a
linear operator M_B on V by M_B(A) = BAB*, where B* is the conjugate transpose of B. Show that det M_B = |det B|^{2n}.

2-H is the set of all Hermitian matrices in V, A being Hermitian if
A=A*.Then H is a vector space over IR.Show that the function T_B
defined by T_B(A)=BAB* is a linear operator on H, and that
detT_B=|det B|^{2n}.

I know that the determinant of M_B is equal to that of the matrix P representing M_B .Can I find this matrix?
For part 2) I know how to show that T_B is a linear operator, and
then I guess I have to find det T_B= det M_B....  Display posts from previous: All Posts1 Day7 Days2 Weeks1 Month3 Months6 Months1 Year Oldest FirstNewest First
 The time now is Sat Mar 23, 2019 10:16 am | All times are GMT Forum index » Science and Technology » Math
 Jump to: Select a forum-------------------Forum index|___Science and Technology    |___Math    |   |___Research    |   |___num-analysis    |   |___Symbolic    |   |___Combinatorics    |   |___Probability    |   |   |___Prediction    |   |       |   |___Undergraduate    |   |___Recreational    |       |___Physics    |   |___Research    |   |___New Theories    |   |___Acoustics    |   |___Electromagnetics    |   |___Strings    |   |___Particle    |   |___Fusion    |   |___Relativity    |       |___Chem    |   |___Analytical    |   |___Electrochem    |   |   |___Battery    |   |       |   |___Coatings    |       |___Engineering        |___Control        |___Mechanics        |___Chemical

 Topic Author Forum Replies Last Post Similar Topics sign of the determinant of an augmented matrix? Mark Math 4 Thu Jul 20, 2006 1:30 am approximating infinite linear programming problems diegotorquemada@yahoo.com Math 0 Mon Jul 17, 2006 10:29 am Operator Overloading (Sets and Numbers) DGoncz@aol.com Math 1 Sun Jul 16, 2006 8:26 pm Angular Momentum Operator Farooq W Math 1 Sun Jul 16, 2006 4:44 pm Linear algebra txtbk recommendations... Snis Pilbor Math 1 Sat Jul 15, 2006 11:40 pm