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  "body": "\n## Summary\n\nA Riesz basis of a [[Hilbert space|HM2HHE3J51]] is the image of an [[orthonormal basis|0S9GGTR0EX]] under a bounded invertible operator.\nIt keeps the main features of an orthonormal basis.\nEvery vector has a unique expansion, and its length is comparable to the length of its coefficient sequence.\nRiesz bases are exactly the bases that are also frames, and they are unconditional [[Schauder bases|528G11SDWR]].\nThey are the natural notion of a stable basis in sampling theory, wavelets and nonharmonic Fourier analysis.\n\n## Explanations\n\n### L1 human\n\nAn orthonormal basis is like a set of perpendicular rulers of length one.\nA Riesz basis is what you get after you stretch and tilt the space by a linear map that can be undone.\nThe rulers are no longer perpendicular or of equal length, but they are not too close to each other either.\nSo coordinates in a Riesz basis are still unique and still control the length of the vector, up to fixed constants.\n",
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