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Operation Layers Merge grouped layers Merge a layer set Merge linked layers Merge all visible layers Copy merged version of selection to Clipboard Clone contents of layer into next layer down Clone contents of linked layers to active layer Clone contents of all visible layers to activate layer Group neighboring layers Ungroup neighboring layers Edit layer style Edit specific style Switch between layer styles in Layer Styles dialog box Clear all layer styles Create adjustment layer Create and name adjustment layer Save flattened copy of layered image Delete linked layers or sets Add Layer Set Add Layer Set with name and blending options -E -E -E -Shift-E -Shift-C -Option-E -Option-E -Option-Shift-E Option-click horizontal line in Layers palette or -G Option-click dotted line in Layers palette or -Shift-G double-click layer double-click specific style in Layers palette -1 through -0 Option-double-click choose from dual-tone icon menu at bottom of Layers palette Option-choose from dual-tone icon menu at bottom of Layers palette -Option-S -click trash icon in Layers palette click folder icon in Layers palette Option-click folder icon in Layers palette Shortcut

Thus, we have eigenpairs ( 0 , x (0) ), ( 1 , x (1) ), ( 2 , x (2) ). We continue to emphasize that in all cases any free parameters are arbitrary, except that they must never be selected to give a zero-valued eigenvector. In Example 11.2 = 1 is an eigenvalue of multiplicity 2, and v (0) is a vector in a two-dimensional vector subspace of C3 . On the other hand, in Example 11.1 = 1 is also of multiplicity 2, and yet v (0) is only a vector in a one-dimensional vector subspace of C3 . De nition 11.2: Defective Matrix For any A Cn n , if the multiplicity of any eigenvalue C is not equal to the dimension of the solution space (eigenspace) of ( I A)x = 0, then A is defective. From this de nition, A in Example 11.1 is a defective matrix, while A in Example 11.2 is not defective (i.e., is nondefective). In a sense soon to be made precise, defective matrices cannot be diagonalized. However, all matrices, diagonalizable or not, can be placed into Jordan canonical form, as follows. Theorem 11.1: Jordan Decomposition singular matrix T Cn n such that If A Cn n , then there exists a non-

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7.2 11.0 19.2

Dimensioning is usually done after you complete all or most of a drawing. When you dimension a drawing all at once, you can create a unified, organized look for your dimensions. Before you can dimension a drawing, you need to understand the elements of a dimension and how to prepare for dimensioning.

The arrow marked X points along the X axis in the positive direction. This means that as you go in the direction of the arrow, the X coordinates increase. The arrow marked Y points along the Y axis in the positive direction.

4.8 3-D LIGHT IMAGING A convention 2-D microscope can be extended to 3-D light imaging using the concept of confocal microscope discussed in Section 3.9.3. A schematic diagram of a uorescence confocal microscope is shown in Figure 4.23. First, the focusing mechanism, a laser beam as the light source (Fig. 4.23, left) is used to scan (x-y scanning mirrors), focus (objective lens), and excite uorescence objects of interest in order to obtain depth discrimination from other objects in the sample. Only the in-focus

Figure 28-17: The DWF file as seen in Autodesk DWF Viewer. 3. Press Ctrl and click 1 in Figure 28-17. The text shown in Figure 28-18 opens in a new Internet Explorer window. (You may have to minimize Autodesk DWF Viewer to see the text.) This comes from an Excel spreadsheet saved in text format. 4. Right-click in the drawing to open the shortcut menu. Choose Zoom Rectangle. Drag a window to zoom in. Choose Pan from the menu, and pan to the left. Choose Fit in Window to return to the previous view. (If you want, choose Print to print the drawing to the system printer.) 5. Press Ctrl and click 2 in Figure 28-17. You see the horizontal angle in a new Internet Explorer window. 6. Close Autodesk DWF Viewer, as well as the Internet Explorer windows.

One of the most interesting form factors for Media Center PCs is the cube. It s very similar in appearance to a mini shelf system stereo. It s a machine that can t just about anywhere due to its small size. (See Figure 2-4.) The smaller size does limit the cube form factor from being as expandable as the tower or desktop. This means you have only one optical drive (such as a DVD-R or CD-RW) rather than the two usually found on towers and desktops, and limited room for extra hard drives and add-on cards. Right now this

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