Linear Algebra - Transposes
Linear Algebra - Transposes
In[]:=
{matrixA={{1,0},{1,1}},matrixB={{5,0},{4,1}}};
The transpose of A + B is A + B
The transpose of A + B is A + B
In[]:=
Transpose[matrixA+matrixB]Transpose[matrixA]+Transpose[matrixB]
Out[]=
True
In[]:=
{Transpose[matrixA+matrixB]//MatrixForm,(Transpose[matrixA]+Transpose[matrixB])//MatrixForm}
Out[]=
,
6 | 5 |
0 | 2 |
6 | 5 |
0 | 2 |
The transpose of A B is (A B) = B A
The transpose of A B is (A B) = B A
In[]:=
Transpose[matrixA.matrixB]==Transpose[matrixB].Transpose[matrixA]
Out[]=
True
In[]:=
.
//MatrixForm,
.
//MatrixForm
1 | 0 |
1 | 1 |
5 | 0 |
4 | 1 |
5 | 0 |
4 | 1 |
1 | 0 |
1 | 1 |
Out[]=
,
5 | 9 |
0 | 1 |
5 | 9 |
0 | 1 |
Thetransposeof-1Ais(-1A)=-1(A)
Thetransposeofis()=
-1
A
-1
A
-1
(A)
In[]:=
Transpose[Inverse[matrixA]]Inverse[Transpose[matrixA]]
Out[]=
True
In[]:=
//MatrixForm,Inverse
//MatrixForm
1 | 0 |
-1 | 1 |
1 | 1 |
0 | 1 |
Out[]=
,
1 | -1 |
0 | 1 |
1 | -1 |
0 | 1 |