# All Questions

208 views

### Question on Intersection Theory of Effective Divisors

I am reading Section 1.1C of Lazarsfeld "Positivity in Algebraic Geometry I" and I need help understanding one line. On Page 17, Remark 1.1.13(iii), he says the following: If $D_1,..., D_n$ are ...
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### similar matrices have the same bandwidth?

If $A$ is symmetric with bandwidth $p$ then $A_+ = Q^{T} A Q$, where $Q$ is orthogonal, is orthogonally similar to $A$. How can we show/prove that $A_+$ also has bandwidth $p$ ?
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### How do you find L of LU for this LU factorization?

$$\begin{bmatrix} 3 & -7 & -2 \\ -3 & 5 & 1 \\ 6 & -4 & 0 \\ \end{bmatrix}$$ The method my book gave me of doing this is: divide col1 ...
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### How prove $\binom{n}{m}\le\left(\frac{en}{m}\right)^m$ [duplicate]

Show that $$\binom{n}{m}\le\left(\dfrac{en}{m}\right)^m$$ where $0<m\le n,m,n\in N^{+}$ My idea: since ...
103 views

### Finding a particular solution to the non-homogenous system

I have the following problem $\vec{x}^{'}(t)=\begin{pmatrix} 2 & -5\\1 & -2 \end{pmatrix}\vec{x} + \begin{pmatrix} \csc t\\ \sec t \end{pmatrix}$ Step 1) Find the Eigenvalues ...
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### Prove $p \times(1 - p)^n$ is a probability function

$p \times (1 - p)^n$ where $p$ is the probability an event will happen after $n$ number of failure attempts. I know I have to show that the sum of the probabilities of all possible events equals one. ...
130 views

### How does one arrive at the asymptotic expressions for the bessel functions?

It is known that Bessel functions for large arguments will behave as exp or cos/sin however I was wondering how does one arrive at those results. The motivation being that I would like to use these ...