Linear Algebra and the Basic Mathematical Tools for Finite-Dimensional Entanglement Theory
نویسنده
چکیده
2 Linear Operators 6 2.1 Outer Products, Adjoints, and Eigenvalues . . . . . . . . . . . . . . . . . . . . . . . . 6 2.2 Important Types of Operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.2.1 Projections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.2.2 Normal Operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.2.3 Unitary Operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.2.4 Hermitian Operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.2.5 Positive Operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.3 Functions of Normal Operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.4 The Polar and Singular Value Decompositions . . . . . . . . . . . . . . . . . . . . . . 14
منابع مشابه
Linear Algebra and the Basic Mathematical Tools for Finite-Dimensional Entanglement Theory - Solutions to Exercises
Exercise 1 Suppose that H = C3 and let V be the one-dimensional subspace spanned by |ψy = ?1/3(|0y+ ei/3|1y |2y). Provide an orthonormal basis for VK. Solution: We need to identify a pair of orthonormal states that are also orthogonal to |ψy. An easy first state to take is |ψK 1 y = 1 2 (|0y ei/3|1y). Any other vector of the form a(|0y+ ei/3|1y+ b|2ywill be orthogonal to |ψK 1 y. To also make i...
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تاریخ انتشار 2018