 Photoshop Lightroom Adobe’s Lightroom is a collection of features that are designed to be an all-in-one photo editing and organizing tool. Like Photoshop, Lightroom is primarily a workbook of layered, raster images, but the user interface is more streamlined and user-friendly. It enables you to import images from anywhere, view images on a computer or on a camera, copy images, crop, clean them up, add text and shapes, and burn images onto DVDs. The features and compatibility of Lightroom work well with a digital SLR because you can import into Lightroom images that you’ve created with your camera’s screen. Its ability to view and manage all your photos, whether in print or online, is a powerful feature that can save time spent going through a bunch of images in search of photos that you want to print. However, Lightroom doesn’t do as much as Photoshop in terms of editing, though it does enable you to create and build collections of images. Some people use it along with Photoshop, and although it’s an Adobe program, it’s a fully featured one. You can check it out at www.adobe.com/lightroom. ## Seeing the Big Picture When you’re choosing a photo editing program, you need to consider what editing features you can expect to find. The programs differ in what is possible, and the cost. Consider the following details when choosing a photo editing program.

), then the eigenvalues of $\Gamma$ are real. Therefore, by Remark $rem:p\_i\_and\_q\_i$, $\Lambda=\pm\bigl(\!\sqrt{\varepsilon}p_i+\sqrt{\varepsilon}q_i\,\bigr)$ for some $i\in\{1,2,3,4\}$. The conclusion is reached by Lemma $lem:lattice$. $prop:eigenvalue\_overlapping$ Let $\mathcal{B}\in{\mathbb{R}}^{m\times n}$ be a banded matrix with $\mathrm{rank}(\mathcal{B})=1$ and let $\alpha\in{\mathbb{R}}\setminus\{0\}$. Then, the eigenvalue $\lambda=\alpha$ of $\mathcal{B}$ is of multiplicity two. Let $i\in\{1,2,3,4\}$ be the index chosen in the proof of Proposition $prop:lattice$. Define $\Lambda$ as in  with $p_i$ and $q_i$ as in . We have $\lambda=\alpha$ and $\lambda$ is of multiplicity two since $\Lambda=\pm\bigl(\!\sqrt{\varepsilon}p_i+\sqrt{\varepsilon}q_i\,\bigr)$. This result is optimal and since Remark $rem:p\_i\_and\_q\_i$ states that $\varepsilon p_i\in\mathrm{Span}(p_1,p_2,p_3)$ and $\varepsilon q_i\in\mathrm{Span}(q_1,q_2,q_3)$, it follows that we cannot have \$\lambda=\pm\bigl(\!\sqrt{\varepsilon}p_i+\sqrt{\vare