Question

Is the standard basis for M22 in real numbers the same as in Complex numbers?

Answer 1

Standard basis for \[M _{22}\] in complex field?

Answer 2

hmm isnt it the vector spaces ?

Answer 3

i had feeling they are the same in real in addition these :-
(0,i)
(1,i)
(i,0)
(i,1)
not sure though

Answer 4

The standard basis for M22 in real number has 4 matrices. The standard basis for M22 in complex number has 8 matrices.

Answer 5

thank you guys. I am trying to get the basis for R(T), where
T(X) = AX

A =

Answer 6

http://math.stackexchange.com/questions/360599/basis-of-complex-matrix-vector-space-over-bbbr

Answer 7

SO in trying to do that I USED the Standard basis for \[M _{22}\] : [1 0 0 0], [0 1 0 0] ,[0 0 1 0] and [ 0 0 0 1] reasoning

R(T) = \[span[ Te _{1} Te _{2}Te _{3}Te _{4}]\]

Answer 8

Thank you @Loser66 , @thomas5267,@marki

Answer 9

yw