- #1
Bacle
- 662
- 1
Hi, Everyone:
In linear algebra courses, the defs/formulas for
the sum, multiplication of matrices respectively,
are often motivated by the fact that matrix addition
models the point-wise addition of linear maps, i.e.,
If A,B are linear maps described on the same basis, then
the sum (a_ij)+(b_ij) describes the linear operator:
(A+B)(x)=A(x)+B(x)
And AB models the composition of the operators A,B;
i.e., A*B(x) =A( B(x)).
Now, I am teaching a class in which matrices have,
so far, been used only to represent systems of linear
equations. Does anyone know how to motivate the
definitions A+B and AB from this or a related
perspective?
Thanks.
In linear algebra courses, the defs/formulas for
the sum, multiplication of matrices respectively,
are often motivated by the fact that matrix addition
models the point-wise addition of linear maps, i.e.,
If A,B are linear maps described on the same basis, then
the sum (a_ij)+(b_ij) describes the linear operator:
(A+B)(x)=A(x)+B(x)
And AB models the composition of the operators A,B;
i.e., A*B(x) =A( B(x)).
Now, I am teaching a class in which matrices have,
so far, been used only to represent systems of linear
equations. Does anyone know how to motivate the
definitions A+B and AB from this or a related
perspective?
Thanks.