SOLVED:(When is a subspace of a complex vector space a complexification?) Let V be a real vector space with complexification V^C and let U be a subspace of V^C. Prove that there is a subspace S of V for which U=S^C={s t i |s, t ∈S} if and only if U is closed under complex conjugation χ: V^C →V^C defined by χ(u i v)=u-i v.
SOLVED:(When is a subspace of a complex vector space a complexif…
1 month ago
numerade.com
SOLVED:Let V denote the complex vector space spanned by the functions 1, e^i x and e^-i x, where x is a real variable. Which of the following functions belong to V ? (a) sinx, (b) cosx-2 i sinx, (c) coshx, (d) sin^2 (1)/(2) x, (e) cos^2 x ?
SOLVED:Let V denote the complex vector space spanned by the funct…
Aug 31, 2023
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Conjugates of Complex Numbers - Properties and Solved Examples
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Let W be the set of all 2 ×2 complex Hermitian matrices, that is, the set of 2 ×2 complex matrices A such that Ai j=Aj i (the bar denoting complex conjugation). As we pointed out in Example 6 of Chapter 2, W is a vector space over the field of real numbers, under the usual operations. Verify that (x, y, z, t) →[ t x y i z y-i z t-x] is an isomorphism of R^4 onto W. | Numerade
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