8 lines
415 B
Markdown
8 lines
415 B
Markdown
# Outer Product
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- operates on two vectors and produces a matrix
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- notation is $`\ket{x}\bra{y}`$
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- $`\ket{x}`$ is a [[ket]]
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- $`\bra{y}`$ is a [[bra]]
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- [[matrix-multiplication]], associates with [[inner-product]]
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- 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 $`\ket{y}`$
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