# Tagged Questions

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### Eigenvalue formula for 4x4 symmetric matrix

Is there a formula/algorithm that is accurate to used in finite precision arithmetic (aka numerical stable ) for small symmetric matrix of size 4x4. Additionally I'm looking if it require similar ...
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### Matrix representation of a linear operator

As I'm studying for my final, my book keeps skipping alot of steps and I don't know how tthey get from point a to point b - probably because its elementary at that stage in the book, except not to me ...
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### Calculating the characteristic polynomial

I'm stuck with this problem, so I've got the following matrix: $$A = \begin{bmatrix} 4& 6 & 10\\ 3& 10 & 13\\ -2&-6 &-8 \end{bmatrix}$$ Which gives me the following ...
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### Calculate the angles between $(1,X),(X,X^2),(X^2,X^3),(X^3,X^4)$ given the inner product $\langle p(x),q(X) \rangle = \int_{-1}^{1} p(X)q(X)dX$

Let $V_4$ be the vector space of all polynomials of degree less than or equal to 4 with the inner product $$\langle p(x),q(X) \rangle = \int_{-1}^{1} p(X)q(X)dX$$ calculate the angles between ...
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### Finding an eigenbasis of an operator.

Consider the operator $T:\mathbf{P}_1\rightarrow\mathbf{P}_1$ by $T(ax+b):=-bx+(2a-3b)$. I want to find out if there is a basis of eigenvectors of this operator $T$. Now, I have no idea what to do, ...
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### Angle between two polynomials

Given the inner product of two polynomials $p(X), q(X) \in P(d)$, where $P(d)$ is the vector space of all polynomials of degree less than or equal to d, with real coefficients, and using the inner ...
Problem: Suppose $p \in \mathcal{P}(\mathbf{C})$ has degree $m$. Prove that $p$ has $m$ distinct roots if and only if $p$ and its derivative $p'$ have no roots in common. My proof so far: If $m=0$, ...