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- W4288364564 abstract "Basic matrices are defined which provide unique building blocks for the class of normal matrices which include the classes of unitary and Hermitian matrices. Unique builders for quantum logic gates are hence derived since a quantum logic gates is represented by, or is said to be, a unitary matrix. An efficient algorithm for expressing an idempotent as a unique sum of rank $1$ idempotents with increasing initial zeros is derived. This is used to derive a unique form for mixed matrices. A number of (further) applications are given: for example (i) $U$ is a symmetric unitary matrix if and only if it has the form $I-2E$ for a symmetric idempotent $E$, (ii) a formula for the pseudo inverse in terms of basic matrices is derived. Examples for various uses are readily available." @default.
- W4288364564 created "2022-07-29" @default.
- W4288364564 creator A5057194835 @default.
- W4288364564 date "2019-04-25" @default.
- W4288364564 modified "2023-09-23" @default.
- W4288364564 title "Unique builders for classes of matrices" @default.
- W4288364564 doi "https://doi.org/10.48550/arxiv.1904.11250" @default.
- W4288364564 hasPublicationYear "2019" @default.
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