Without using anything from the above two results show that for any complex inner- product (·, ·)v on a complex vector space V, there is a basis U {u1,..., Un} so that (x, y)v = [y]#[æ]u In other words for any finite dimensional inner-product space, there is a choice of basis, so that with respect to that basis, the inner-product is represented by the standard inner-product.

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Q: For vectors, v0= (0,3,4,2),v1= (1,1,2,1), v2= (1,0,0,0), v3= (0,0,1,0), find an orthonormal basis,…

A: Solution by using Gram Schmidt process as follows :

Q: 11 In the standard basis the coordinates of a vector are Xs -7 - (E) 2 In which of the bases given…

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Q: need help on this question   given the basis B={[12],[25]} of R2.{"version":"1.1","math":"\mbox…

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Q: = √1 = Let 4] 2 V2 - 2 and 3 = 2 -7 Explain that B = (V1, V2, V3) forms a basis of a 3-dimensional…

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Q: ) Consider the vectors -- () --- () --- () a= = Do these vectors form a basis of R³? If yes, prove…

A: Please comment if you need any clarification. If you find my answer useful please put thumbs up.…

Q: Please discuss your understanding of what a basis is for a vector space

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Q: Is the set swer. {(1,2,-1,3), (1,-1, 2, 0), (-2, 0, 6, 6)} a basis for R¹? Justify your an-

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Q: Are the following vectors a basis of R²?

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Q: Find an orthonormal basis of the plane x1+ 5x2 – x3 = 0. }

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Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.