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.

Now I am studying linear algebra course, In that for a given matrix we are finding the characteristic values (eigen values) and characteristic vectors (eigen vectors). But my question is why cant we find a matrix by the characteristic values and vectors ?

share|improve this question

migrated from mathematica.stackexchange.com Apr 16 at 15:24

This question came from our site for users of Mathematica.

Is this a question about mathematics, or the software Mathematica? This site is for the latter. –  Simon Woods Apr 16 at 14:14

1 Answer 1

You should note that for a diagonalizable matrix $\mathbf{M}$, the following equality holds:


Where $\mathbf{\Lambda}=\operatorname{diag}(\lambda_{1},\cdots,\lambda_{n})$, and $\lambda_{i}$ is the $i$th eigenvalue; and $\mathbf{P}$ is the matrix formed by the eigenvectors, i.e:

$$\mathbf{P}=\begin{pmatrix}\uparrow && \uparrow \\ v_{1} & \cdots & v_{n} \\ \downarrow && \downarrow\end{pmatrix}$$

You can use this to find $\mathbf{M}$ from the eigenvalues and eigenvectors.

share|improve this answer

Your Answer


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