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twinphoton
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What is the so called "orthogonal operator basis"?
What is the so called "orthogonal operator basis"?
What is the so called "orthogonal operator basis"?
arunma said:I've never heard of the orthogonal operator basis, though I assume it would be a field theory thing, since in QFT we turn the wavefunctions into operators. I could be wrong.
Are you sure you're not simply talking about an orthogonal basis?
An orthogonal operator basis is a set of linear operators that are orthogonal to each other, meaning they have a dot product of zero. This is similar to how orthogonal vectors are perpendicular to each other in Euclidean space.
An orthogonal operator basis is important because it allows for the simplification of complex linear transformations and makes it easier to perform calculations. It also allows for the representation of any vector in a vector space using a linear combination of the basis vectors.
An orthogonal operator basis is different from a regular basis in that the basis vectors are not only linearly independent, but also orthogonal to each other. This means that they are not just spanning a vector space, but they are also perpendicular to each other.
Some examples of orthogonal operator bases include the standard basis in Euclidean space, the Fourier basis in signal processing, and the Pauli matrices in quantum mechanics.
To find an orthogonal operator basis for a given vector space, you can use the Gram-Schmidt process. This involves starting with a set of linearly independent vectors and then using orthogonalization to find a set of orthogonal vectors. These orthogonal vectors can then be normalized to create an orthogonal operator basis.