Linear Algebra and the Basic Mathematical Tools for Finite-Dimensional Entanglement Theory - Solutions to Exercises
نویسنده
چکیده
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 it orthogonal to |ψy, we choose |ψK 2 y = 2 (|0y+ ei/3|1y)+ 1 2 |2y. Hence t|ψK 1 y, |ψK 2 yu provides an orthonormal basis for VK.
منابع مشابه
Linear Algebra and the Basic Mathematical Tools for Finite-Dimensional Entanglement Theory
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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...
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