| Differences between revisions 1 and 2 | Back to page |
|
⇤ ← Revision 1 as of 9:18AM, Sep 27, 2011
Size: 578
Comment:
|
Size: 580
Comment:
|
| Deletions are marked like this. | Additions are marked like this. |
| Line 6: | Line 6: |
Linear transformation and matrix
A matrix represents a linear transformation of vectors. Is the reverse true? Namely, can any linear transformation (of a finite dimensional vectors) be represented by a matrix?
- Yes B. No
Matrix and linear transformation
Suppose that a linear transformation of a 2D vector space maps $\bigl(\begin{smallmatrix} 1 \\ 0 \end{smallmatrix} \bigr)$ to $\vec{a}$, and $\bigl(\begin{smallmatrix} 0 \\ 1 \end{smallmatrix} \bigr)$ to $\vec{b}$. The matrix that represents this linear transformation is
- Yes B. N