The transpose of a matrix is the matrix formed by “flipping” about the diagonal line from the upper left corner. It is usually denoted , although sometimes it is written as or . So if is an matrix and
Note that the transpose of an matrix is a matrix.
Let and be matrices, and be matrices, be an matrix, and be a constant. Let and be column vectors with rows. Then
If is invertible , then
If is real, (where is the trace of a matrix).
The familiar vector dot product can also be defined using the matrix transpose. If and are column vectors with rows each,
which is another way of defining the square of the vector Euclidean norm.
|Date of creation||2013-03-22 12:01:02|
|Last modified on||2013-03-22 12:01:02|
|Last modified by||mathcam (2727)|