# Equivalent matrix?

1. May 6, 2007

### pivoxa15

1. The problem statement, all variables and given/known data
How do you turn the transformation matrix

1+i 3
2-i 5i

into a diagonal matrix when it is transforming vectors in the Z module?

What is the Z module? Normally one states R module M. where R is the coefficient one multiplies to the elements in the module.

3. The attempt at a solution
I have tried but can't seem to reduce to diagonal form as I can only multiply by integer numbers?

2. May 6, 2007

### pivoxa15

I have just worked out the diagonal matrix. It is

1 0
0 8+11i

However my question of what is the Z module still stands. I know clearly what a Z ring is.

3. May 6, 2007

### HallsofIvy

Staff Emeritus
Z is the same whether you think of it as a ring or a module- the "Gaussian integers"- all numbers of the form a+ bi where a and b are integers and i is, of course, the imaginary unit.

4. May 6, 2007

### pivoxa15

I think that the Z module is refering to any module where the coefficients are from the ring of the Gaussian integers. Why use the word Gaussian?