The Picard ManeuverM to memes • 6 months agoThey keep digging that hole deeperimagemessage-square88arrow-up1844arrow-down136
arrow-up1808arrow-down1imageThey keep digging that hole deeperThe Picard ManeuverM to memes • 6 months agomessage-square88
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.