Let E be an identity matrix with appropriate dimension, +3,2+3, (+3), 2+2+5j, 2+2-5j, (2+2+5j), (2+2-5j),...

 

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Let E be an identity matrix with appropriate dimension, λ +3,2+3, (+3)², 2+2+5j, 2+2-5j, (2+2+5j)², (2+2-5j)², are elementary divisors for E-A. (1) Find out the Smith canonical form for E-A, the Natural normal form N and the Jordan canonical form for A. (2) Let A₁ = -3,2₂ = -2+5i, 3 = -2- 5i, Y₁ = {y|(AAE)" y = 0, for some m € Z+,0} Z+0 is the set of non-negative integers, show that y₁ = ker[(AAE)2],i = 1,2,3, and determine the corresponding dimensions dimy,, i = 1,2,3. Let E be an identity matrix with appropriate dimension, λ +3,2+3, (+3)², 2+2+5j, 2+2-5j, (2+2+5j)², (2+2-5j)², are elementary divisors for E-A. (1) Find out the Smith canonical form for E-A, the Natural normal form N and the Jordan canonical form for A. (2) Let A₁ = -3,2₂ = -2+5i, 3 = -2- 5i, Y₁ = {y|(AAE)" y = 0, for some m € Z+,0} Z+0 is the set of non-negative integers, show that y₁ = ker[(AAE)2],i = 1,2,3, and determine the corresponding dimensions dimy,, i = 1,2,3. Let E be an identity matrix with appropriate dimension, λ +3,2+3, (+3)², 2+2+5j, 2+2-5j, (2+2+5j)², (2+2-5j)², are elementary divisors for E-A. (1) Find out the Smith canonical form for E-A, the Natural normal form N and the Jordan canonical form for A. (2) Let A₁ = -3,2₂ = -2+5i, 3 = -2- 5i, Y₁ = {y|(AAE)" y = 0, for some m € Z+,0} Z+0 is the set of non-negative integers, show that y₁ = ker[(AAE)2],i = 1,2,3, and determine the corresponding dimensions dimy,, i = 1,2,3. Let E be an identity matrix with appropriate dimension, λ +3,2+3, (+3)², 2+2+5j, 2+2-5j, (2+2+5j)², (2+2-5j)², are elementary divisors for E-A. (1) Find out the Smith canonical form for E-A, the Natural normal form N and the Jordan canonical form for A. (2) Let A₁ = -3,2₂ = -2+5i, 3 = -2- 5i, Y₁ = {y|(AAE)" y = 0, for some m € Z+,0} Z+0 is the set of non-negative integers, show that y₁ = ker[(AAE)2],i = 1,2,3, and determine the corresponding dimensions dimy,, i = 1,2,3.

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3 For the case k 3 find out the different possible Smith canonical forms for A 1 ... View the full answer