# How do I enter an imaginary number into a matrix

In a very simple example, I am created a 2 by 2 matrix like this

var('i')
ran40 = matrix(QQ,2,2,[[2*i,-2],[3,4]])
show(ran40)


I need to eventually call show(ran40.rref()) so that I can see the reduced row echelon form of the above matrix. But I get syntax errors in the creation of the matrix above.

How do I simply put the imaginary letter i into a matrix and then it actually be computed on. That is, the imaginart "part" is actually used in the RREF computation.

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( 2016-02-25 08:47:49 -0500 )edit

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When you write var('i'), you define i as a symbol. In particular, 2*i is an element of the symbolic ring, not the rationals, but you ask that 2*i be an entry of a matrix whose coefficients are rationals (because of the QQ at the beginnig).

If you want the imaginary number, you should use the already defined I, if you want a matrix over, say the algabraic numbers QQbar (so that I in an element), you should write:

sage: matrix(QQbar,2,2,[[2*I,-2],[3,4]])
[2*I  -2]
[  3   4]

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