Matrix transpose

Summary

• Transpose: If \(A\) is \(n×m\) with elements \(a_{i,j}\) then the transpose of \(A\) , denoted by \(A^T\) or \(A'\) is an \(m×n\) matrix with elements \(a_{j,i}\) .
• We say that \(A\) is symmetric if \(A\) is square and \(A^T=A\)
• \({\left( A^T \right)}^T=A\)
• \({\left( αA \right)}^T=αA^T\)
• \({\left( A+B \right)}^T=A^T+B^T\)
• \({\left( AB \right)}^T=B^TA^T\)