Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

please see the following picture and tell me if you know the solution. Thank you very much.!

enter image description here

share|improve this question

1 Answer 1

If $B$ is the matrix of your basis vectors (as column vectors) then to find the coordinates of any $\vec{x}$ in the new basis $B$, you have $B \vec{x}_B = \vec{x}$, therefore you could compute $\vec{x}_B = B^{-1} \vec{x}$ or, more efficiently on the computer, solve the system by Gaussian Elimination.

In your case, you may combine a couple of vectors into a matrix, to do this in parallel. In other words, to solve a couple like that, let $V$ be the matrix of column-vectors you want in the new basis, then $V_B = B^{-1}V$.

EDIT 1 Here is the more detailed version. Get or implement a routine to run Gaussian Elimination (pseudocode on the Wiki page, most libraries support it). That solves the system $A \vec{z} = \vec{x}$ given $A$ and $\vec{x}$. This should also support solving this system simultaneously for multiple vectors, i.e.

$$A \left[ \vec{z_1} | \ldots | \vec{z}_n \right] = \left[ \vec{x_1} | \ldots | \vec{x}_n \right]$$

given $A$ and the vectors $\vec{x_1}, \ldots, \vec{x}_n$.

Now for your problem. You have three vectors in regular coordinates $(1,0)^T, (0,1)^T, (1,1)^T$ which you need to express as a linear combination of vectors in your new basis $B$, so let these 3 be the vectors you know ($\vec{x}$'s) and use Gaussian Elimination to solve $B Z = X$, where $X$ and $B$ are known and you need to find $Z$ - that would get you all the coordinates of each of the vectors you want in terms of your new coordinates $B$.

share|improve this answer
Thank you, it is quite hard for me to understand because I haven't used a matrix and mathematical shorthand for many years, I would understand very well in code however :) –  comprehensible Mar 20 '13 at 19:54
@ufomorace Please see the edit. –  gt6989b Mar 20 '13 at 20:12

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.