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Calculate matrix transpose A^T, check symmetric and skew-symmetric matrices, and verify transpose properties. 100% client-side—no data sent to servers. Supports matrices up to 10×10.
This matrix transpose calculator computes A^T by swapping rows and columns. All computations run client-side in your browser—no matrices are sent to any server. Supports symmetric and skew-symmetric detection, property checks, and step-by-step solutions up to 10×10.
The transpose A^T is obtained by swapping rows and columns: (A^T)ij = Aji. If A is m×n, then A^T is n×m. Key rules: (A^T)^T = A, (A+B)^T = A^T + B^T, and (AB)^T = B^T A^T.
A matrix is symmetric when A = A^T and skew-symmetric when A = -A^T (all diagonal entries are zero). This tool flags these properties automatically.
For square matrices, det(A^T) = det(A) and rank(A^T) = rank(A). Transpose preserves determinant magnitude and rank.
A symmetric matrix satisfies A = A^T (mirror across diagonal). A skew-symmetric matrix satisfies A = -A^T (diagonal must be zero). Every square matrix can be decomposed as the sum of a symmetric and skew-symmetric part.