Let A ∈ M2×2(R). For u, v ∈ R2, definefA(u, v) = utAv.(Here we are taking u and v to be 2 × 1 column vectors.) Show that fA defines aninner product on R2if and only if A = At, a11 > 0, a22 > 0, and det A > 0.
Let A ∈ M2×2(R). For u, v ∈ R2, definefA(u, v) = utAv.(Here we are taking u and v to be 2 × 1 column vectors.) Show that fA defines aninner product on R2if and only if A = At, a11 > 0, a22 > 0, and det A > 0.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Let A ∈ M2×2(R). For u, v ∈ R
2
, define
fA(u, v) = u
tAv.
(Here we are taking u and v to be 2 × 1 column
inner product on R
2
if and only if A = At
, a11 > 0, a22 > 0, and det A > 0.
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