Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

I have to determine the $Matrix F$ which describes f in comparison to the base A(a1,a2,a3,a4), and the matrix B - which describes regarding the basis E=(e1,e2,e3,e4) for $R^4$ That is
$F =a[f]a$

From a previous calculation, i know that:

$f(x)=(x \cdot a1)a2+(x \cdot a2)a3 +(x \cdot a3)a4$
Where $a1,a2...$ is vectors forming an orthogonal basis $R^4$

But I dont get the meaning of F=a[f]a

share|cite|improve this question
Too confusing. Do you have two basis for $\mathbb{R}^4$ and you want to write the matrix of the map $f$? – Sigur Dec 27 '12 at 16:43
Sorry for the confusion. Yeah I have two basis for $R^4$ E(e1,e2,e3,e4) and A(a1,a2,a3,a4). – user54425 Dec 27 '12 at 16:47
To determine the matrix you should apply the map on the base, write the image as linear combinations of the base and transpose to obtains the matrix. – Sigur Dec 27 '12 at 16:49
Could u elaborate how to map on the base? Thanks btw – user54425 Dec 27 '12 at 16:52
up vote 0 down vote accepted

I don't understand you notation, but I believe that you want $F:=[f]_A^A$, the matrix of the map $f:(\mathbb{R}^4,A)\to (\mathbb{R}^4,A)$ where $A=\{a_1,\ldots, a_4\}$ is a base for $\mathbb{R}^4$.

Also similar for the other base.

Well, if this is the case, you have to compute $f(a_i)$ (using the definition of $f$) and write it as linear combination of vectors on $A$, that is, $$f(a_i)=\sum_{j=1}^4\alpha_{ij}a_j, \quad 1\leq i\leq 4.$$ Then you write the matrix $$F:=[f]_A^A=\begin{pmatrix}\alpha_{11} & \cdots & \alpha_{41} \\ \vdots & \ddots & \vdots \\ \alpha_{14} & \cdots & \alpha_{44}\end{pmatrix}.$$

share|cite|improve this answer
Thanks man I will try and then respond :) – user54425 Dec 27 '12 at 17:04
Not sure i quite got it Is that anything near? I plotted the f(x) in Maple as M(m). – user54425 Dec 27 '12 at 17:58
By definition, $f(a_1)=(a_1\cdot a_1)a_2+ (a_1\cdot a_2)a_3+ (a_1\cdot a_3)a_4$. So its coordinates are $f(a_1)=(0,a_1\cdot a_1, a_1\cdot a_2,a_1\cdot a_3)$. If the base $A$ is orthonormal, then you get $(0,1,0,0)$. – Sigur Dec 27 '12 at 18:05
Ah u simply get f(a1),f(a2),f(a3),f(a4) and put them in the rows of F? – user54425 Dec 27 '12 at 20:21 – user54425 Dec 27 '12 at 20:38

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.