H13-311_V3.5 · Question #271
The trace operation returns the sum of the diagonal elements of the matrix. Therefore, the trace of matrix A and its transposed matrix are equal
The correct answer is A. True. A is correct because transposing a matrix swaps rows and columns, but leaves the main diagonal (where row index equals column index) completely unchanged. Since the trace sums only those diagonal elements, tr(A) = tr(Aᵀ) always holds. B is wrong because it assumes transposition…
Question
The trace operation returns the sum of the diagonal elements of the matrix. Therefore, the trace of matrix A and its transposed matrix are equal
Options
- ATrue
- BFalse
How the community answered
(35 responses)- A74% (26)
- B26% (9)
Explanation
A is correct because transposing a matrix swaps rows and columns, but leaves the main diagonal (where row index equals column index) completely unchanged. Since the trace sums only those diagonal elements, tr(A) = tr(Aᵀ) always holds.
B is wrong because it assumes transposition somehow alters the diagonal - it does not. Off-diagonal elements swap positions, but the diagonal elements stay fixed in place.
Memory tip: Think of the diagonal as the "spine" of the matrix - when you fold the matrix along its spine to transpose it, the spine itself doesn't move. The trace only reads the spine, so it's always the same before and after the fold.
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