The Picard ManeuverM to [email protected] • 6 months agoThey keep digging that hole deeperlemmy.worldmessage-square85fedilinkarrow-up1839
arrow-up1839imageThey keep digging that hole deeperlemmy.worldThe Picard ManeuverM to [email protected] • 6 months agomessage-square85fedilink
minus-squareKogasalinkfedilink2•edit-26 months agoYup, you’ll notice the only thing distinguishing C from R^(2) is that multiplication. That one definition has extremely broad implications. For fun, another definition is in terms of 2x2 matrices with real entries. The identity matrix 1 0 0 1 is identified with the real number 1, and the matrix 0 1 -1 0 is identified with i. Given this setup, the normal definitions of matrix addition and multiplication define the complex numbers.
Ok, that’s actually quite interesting
Yup, you’ll notice the only thing distinguishing C from R^(2) is that multiplication. That one definition has extremely broad implications.
For fun, another definition is in terms of 2x2 matrices with real entries. The identity matrix
is identified with the real number 1, and the matrix
is identified with i. Given this setup, the normal definitions of matrix addition and multiplication define the complex numbers.