на 1) A) Let V and w be vector spaces such that dim (V) = dim (W) and let T:V->w be linear. Show there exists ordered bases B and I For V and w, respectively, such that [T] is a diagonal matrix.
на 1) A) Let V and w be vector spaces such that dim (V) = dim (W) and let T:V->w be linear. Show there exists ordered bases B and I For V and w, respectively, such that [T] is a diagonal matrix.
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter5: Inner Product Spaces
Section5.2: Inner Product Spaces
Problem 101E: Consider the vectors u=(6,2,4) and v=(1,2,0) from Example 10. Without using Theorem 5.9, show that...
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In linear algebra, one important concept is that of diagonalizability of a linear transformation. As per the question we are given two vector spaces V and W of equal dimension and a linear transformation T : V → W, we aim to show that there exist ordered bases B and γ for V and W, respectively, such that the matrix representation [T]Bγ is a diagonal matrix. In other words, we want to show that T can be diagonalized.
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