This paper concentrates on the primary theme of LET B BE THE SET OF ORTHONORMAL BASES FOR A REAL INNER PRODUCT SPACE V , AND LET I BE THE SET… in which you have to explain and evaluate its intricate aspects in detail. In addition to this, this paper has been reviewed and purchased by most of the students hence; it has been rated 4.8 points on the scale of 5 points. Besides, the price of this paper starts from £ 40. For more details and full access to the paper, please refer to the site.
1. Let B be the set of orthonormal bases for a real inner product space V , and let I be the set of orthogonal vector space isomorphisms S : Fn → V . Define φ : B → I by φ(X) = LX for all X ∈ B. Prove or disprove: φ is a bijection.
2. Let B be the set of ordered bases for V , and let I be the set of F-algebra isomorphisms S : L(V ) → Mn(F). Define φ : B → I by φ(X) = MX, where MX(T) = [T]X for T ∈ L(V ). Determine (with proof) whether φ is injective or surjective.