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What is the matrix of the transpose map M2×2(F) → M2×2(F) with respect to the "standard basis" of M2x2(F)?

What is the matrix of the transpose map M2×2(F) → M2×2(F) with respect to the "standard basis" of M2x2(F)?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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What is the matrix of the transpose map \( M_{2 \times 2}(\mathbb{F}) \to M_{2 \times 2}(\mathbb{F}) \) with respect to the “standard basis” of \( M_{2 \times 2}(\mathbb{F}) \)?
Transcribed Image Text:What is the matrix of the transpose map \( M_{2 \times 2}(\mathbb{F}) \to M_{2 \times 2}(\mathbb{F}) \) with respect to the “standard basis” of \( M_{2 \times 2}(\mathbb{F}) \)?
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Step 1

Given linear transformation is

T(A) = AT

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