| 31. | Orthogonality is viewed as desirable by some researchers because it minimizes redundancy between the dimensions.
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| 32. | Using a lattice basis, neither orthogonality nor unit length is guaranteed, only independence.
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| 33. | Under this new regime orthogonality became undesirable.
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| 34. | Preserving orthogonality requires that it is a rotation that leaves the sub-space invariant.
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| 35. | They satisfy well-defined orthogonality relations.
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| 36. | The orthogonality ensures that they do not interfere with each other and can be sent simultaneously.
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| 37. | Here, the projections are accomplished by the orthogonality of the solenoidal and irrotational function spaces.
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| 38. | Not all projections that preserve the orthogonality of parallels and meridians are angle-preserving .)
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| 39. | Orthogonality allows a suitable basis set of vectors to represent the state of the quantum system.
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| 40. | The author applies these results to generalized orthogonality relations and thence to Riesz and Hilbert spaces.
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