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- W4387319699 abstract "Hermitian operators and unitary operators are quite often encountered in mathematical physics and, in particular, quantum physics. In this chapter we investigate their basic properties. Both Hermitian operators and unitary operators fall under the category of normal operators. The normal matrices are characterized by an important fact that those matrices can be diagonalized by a unitary matrix. Moreover, Hermitian matrices always possess real eigenvalues. This fact largely eases mathematical treatment of quantum mechanics. In relation to these topics, in this chapter we investigate projection operators systematically. We find their important application to physicochemical problems in Part IV. We further investigate Hermitian quadratic forms and real symmetric quadratic forms as an important branch of matrix algebra. In connection with this topic, positive definiteness and non-negative property of a matrix are an important concept. This characteristic is readily applicable to theory of differential operators, thus rendering this chapter closely related to basic concepts of quantum physics." @default.
- W4387319699 created "2023-10-04" @default.
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- W4387319699 date "2023-01-01" @default.
- W4387319699 modified "2023-10-05" @default.
- W4387319699 title "Hermitian Operators and Unitary Operators" @default.
- W4387319699 doi "https://doi.org/10.1007/978-981-99-2512-4_14" @default.
- W4387319699 hasPublicationYear "2023" @default.
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