Matrix Transpose Calculator

Your details

Number of rows in the original matrix (m).
Number of columns in the original matrix (n).
Separate columns with spaces or commas, separate rows with semicolons. Fractions like 3/4 are allowed.
Total entriesNon-symmetric
9

Number of entries (unchanged by transposition: m x n)

Transposed rows3
Transposed columns3
Trace (diagonal sum)15
Symmetry propertyNeither symmetric nor skew-symmetric
Transposed matrix[1, 4, 7; 2, 5, 8; 3, 6, 9]
Transposed rows3
Transposed columns3
Total entries9

Transposed matrix is 3x3. No special symmetry detected.

  • The original matrix has 3 rows and 3 columns. After transposing, it has 3 rows and 3 columns.
  • The trace (sum of diagonal entries) is 15. The trace is always equal for A and A^T, so transposing does not change it.
  • Transposing twice returns the original matrix, that is (A^T)^T = A, always.

Next stepTo check if two matrices commute under transposition, verify whether (AB)^T = B^T A^T holds, which it always does.

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