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Square Root of a Matrix
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Geliefert zwischen Di., 27.01.2026 und Mi., 28.01.2026
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, the square root of a matrix extends the notion of square root from numbers to matrices. In linear algebra and operator theory, given a bounded positive semidefinite operator (a non-negative operator) T on a complex Hilbert space, B is a square root of T if T = B B, where B denotes the Hermitian adjoint of B. According to the spectral theorem, the continuous functional calculus can be applied to obtain an operator T such that T is itself positive and (T )2 = T. The operator T is the unique non-negative square root of T. A bounded non-negative operator on a complex Hilbert space is self adjoint by definition. So T = (T ) T . Conversely, it is trivially true that every operator of the form B B is non-negative. Therefore, an operator T is non-negative if and only if T = B B for some B (equivalently, T = CC for some C). The Cholesky factorization is a particular example of square root.
Weitere Informationen
- Allgemeine Informationen
- GTIN 09786131232831
- Editor Lambert M. Surhone, Mariam T. Tennoe, Susan F. Henssonow
- Größe H220mm x B220mm
- EAN 9786131232831
- Format Fachbuch
- Titel Square Root of a Matrix
- Herausgeber Betascript Publishing
- Anzahl Seiten 76
- Genre Mathematik
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