garden/outer-product.md
2025-09-15 09:48:28 -06:00

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Outer Product

  • operates on two vectors and produces a matrix
  • notation is `\ket{x}\bra{y}`
    • `\ket{x}` is a ket
    • `\bra{y}` is a bra
  • matrix-multiplication, associates with inner-product
  • a sum `\ket{x}\bra{0} + \ket{y}\bra{1}` where `\ket{x}` and `\ket{y}` are orthonormal produces a unitary-operator sending `\ket{0}` to `\ket{x}` and `\ket{1}` to `\ket{y}`