Hamilton quaternions- kernels and images

Assignment Help Mathematics

Reference no: EM13124404

Hamilton Quaternions : Kernels and Images

Show that the map phi: H->M_2(C) defined by phi(a+bi+cj+dk)=(a+b(sqrt -1),c+d(sqrt-1);-c+d(sqrt-1),a-b(sqrt-1)) is a ring homomorphism. Calculate its kernel and describe its image.

Ps. Here H is the ring of integral Hamilton Quaternions and M_2(C) are 2x2 matrices with complex coefficients. notation after the equal sign in the definition of phi is a matrix with the first row of two elements a+b(sqrt-1) and c+d(sqrt-1) and second row of two elements
-c+d(sqrt-1) and a-b(sqrt-1)

Reference no: EM13124404

Questions Cloud

What is the total pressure in the container at equilibrium : At a certain temperature, the Kp for the decomposition of H2S is 0.726 H2S = H2+S initally only H2S is present at a pressure of 0.126 atm in a closed container.

Taxable income from business operations : Which of the following statements most accurately defines taxable income from business operations?

Pay for the bands expenses : In truth, not enough to pay for the band's expenses. For his taxes, Rocky receives Form 1099 Misc for his music performances.

Illustrate what is the rationale of the gasb : Illustrate what is the rationale of the GASB for requiring two sets of financial statements, each with a different measurement focus and basis of accounting for governmental activities?

Hamilton quaternions- kernels and images : Hamilton Quaternions : Kernels and Images, Show that the map phi: H->M_2(C) defined by phi(a+bi+cj+dk)=(a+b(sqrt -1),c+d(sqrt-1);-c+d(sqrt-1),a-b(sqrt-1)) is a ring homomorphism

What is the amount of sj corporations loss : Jennie purchased 50 percent of the shares of SJ Corporation, a calendar year S corporation, for $7,000. She also guaranteed a corporate loan of $6,000. For 2011, SJ Corporation had an operating loss of $22,000. What is the amount of SJ Corporation..

What was the initial concentration : A zero-order reaction has a constant rate of 3.20×10-4 . If after 60.0 seconds the concentration has dropped to 6.50×10-2 , what was the initial concentration?

Short paragraph comparing bruck''s article to koch''s : Write a summary of the piece and pick out the strengths and weaknesses. Write a short paragraph comparing Bruck's article to Koch's, and state which article you think is stronger and more persuasive and is why.

System of squared equations : Please solve for the following system of equations. Include all of the steps which are involved:

User Account

All Pages