Matrix Transpose Calculator

Pick the Size of the Matrix

2x2
3x3
4x4
5x5
6x6
7x7
8x8

Basic Information

Definition: The transpose of a matrix \(A\), written \(A^T\), is the matrix obtained by writing the columns of A, in order, as rows. That is, if \(A=[a_{ij}]\) is an \(m \times n\) matrix, then \(A^T=[b_{ji}]\) is the \(n \times m\) matrix where \(b_{ij}=a_{ji}\)

Few theorems that may facilitate calculations of matrix transpose:
a) \((A + B)^T = (A + B)^T\);
b) \((A^T)^T = A\);
c) \((kA)^T = kA^T\);
d) \((AB)^T = A^T B^T\);.
Our favorite Linear Algebra textbooks:
Book Cover
Schaum's Series - Linear Algebra
Buy from Amazon!
Book Cover
Steven Leon - Linear Algebra with Applications
Buy from Amazon!
Book Cover
D. C. Lay - Linear Algebra and its Applications
Buy from Amazon!
Book Cover
Gilbert Strang - Linear Algebra and Learning from Data
Buy from Amazon!