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An Intuitive Guide to Linear Algebra
If You're an Educator Download instructor resources Additional order info. Overview Order Downloadable Resources Overview. Description These slides present key concepts and definitions from 25 core sections of text. In addition, about 75 color figures from the text are available as PowerPoint slides. Download Resources.A nurse is caring for a client who is receiving filgrastim
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Submit Search. Home Explore. Successfully reported this slideshow. We use your LinkedIn profile and activity data to personalize ads and to show you more relevant ads. You can change your ad preferences anytime. Linear algebra. Upcoming SlideShare. Like this presentation? Why not share! Embed Size px. Start on.Tech Tip: Linear Slides Value Series - Quick Start
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Grade-school algebra explores the relationship between unknown numbers. Straight lines are predictable. Imagine a rooftop: move forward 3 horizontal feet relative to the ground and you might rise 1 foot in elevation The slope! Contrast this with climbing a dome: each horizontal foot forward raises you a different amount. In math terms, an operation F is linear if scaling inputs scales the output, and adding inputs adds the outputs:.
An operation is a calculation based on some inputs. Which operations are linear and predictable? Multiplication, it seems. We doubled the input but quadrupled the output. We doubled the input and did not double the output. So, what types of functions are actually linear?
Limiting ourselves to linear operations has its advantages. Most courses hit you in the face with the details of a matrix. Select a subject, verb and object. Next, conjugate the verb.Mazda bt 50 intercooler hose
Next, how should we track our operations? We could abbreviate the entire function as 3, 4, 5. We know to multiply the first input by the first value, the second input by the second value, the third input by the third value, and add the results. We could try this:.Gilbert Strang linearalgebrabook gmail.
I hope this website will become a valuable resource for everyone learning and doing linear algebra. Here are key links:. My friend Pavel Grinfeld at Drexel has sent me a collection of interesting problems -- mostly elementary but each one with a small twist. These are part of his larger teaching site called LEM. This video standard describes a system for encoding and decoding a "Codec" that engineers have defined for applications like High Definition TV. It is not expected that you will know the meaning of every word -- your book author does not know either.
The point is to see an important example of a "standard" that is created by an industry after years of development so all companies will know what coding system their products must be consistent with. The words "motion compensation" refer to a way to estimate each video image from the previous one. The simplest would be to guess that successive video images are the same. Then we would only need the changes between frames -- hopefully small.
But if the camera is following the action, the whole scene will shift slightly and need correction. A better idea is to see which way the scene is moving and build that change into the next scene.
In fact the motion is allowed to be different on different parts of the screen. It is ideas like this -- easy to talk about but taking years of effort to perfect -- that make video technology and other technologies possible and successful. Engineers do their job. I hope these links give an idea of the detail needed. This page has been accessed at least times since January Here are key links: Table of Contents Preface Section 1.
Linear Algebra Problems in Lemma My friend Pavel Grinfeld at Drexel has sent me a collection of interesting problems -- mostly elementary but each one with a small twist.Nationalities with attached earlobes
Linear Algebra and Matrix. Upcoming SlideShare. Like this presentation? Why not share! Embed Size px. Start on. Show related SlideShares at end. WordPress Shortcode. Published in: EducationTechnology.
Full Name Comment goes here. Are you sure you want to Yes No. No problem. I usually order a research paper or English essay here and there. Scott Filostin You have to choose carefully. I highly recommend them.Specifically, instead of treating each group separately, and analyzing raw scores, we can look only at the differences between the two measures (e. By subtracting the first score from the second for each subject and then analyzing only those "pure (paired) differences," we will exclude the entire part of the variation in our data set that results from unequal base levels of individual subjects.
This is precisely what is being done in the t-test for dependent samples, and, as compared to the t-test for independent samples, it always produces "better" results (i.
If these assumptions are clearly not met, then one of the nonparametric alternative tests should be used. Technically, we can apply the t-test for dependent samples to any two variables in our data set. However, applying this test will make very little sense if the values of the two variables in the data set are not logically and methodologically comparable.
Following, is an example of a data set that can be analyzed using the t-test for dependent samples. WCC before WCC after case 1 case 2 case 3 case 4 case 5. However, the t-test for dependent samples analysis is performed only on the paired differences"ignoring" the raw scores and their potential differentiation.
Thus, the size of this particular difference of 1 will be compared not to the differentiation of raw scores but to the differentiation of the individual difference scores, which is relatively small: 0. Compared to that variability, the difference of 1 is extremely large and can yield a highly significant t value.
If there are more than two "correlated samples" (e. The repeated measures ANOVA can be considered a generalization of the t-test for dependent samples and it offers various features that increase the overall sensitivity of the analysis. The breakdowns analysis calculates descriptive statistics and correlations for dependent variables in each of a number of groups defined by one or more grouping (independent) variables.
In the following example data set (spreadsheet), the dependent variable WCC (White Cell Count) can be broken down by 2 independent variables: Gender (values: males and females), and Height (values: tall and short). GENDER HEIGHT WCC case 1 case 2 case 3 case 4 case 5. The resulting breakdowns might look as follows (we are assuming that Gender was specified as the first independent variable, and Height as the second).
For example, in the above example, you see the means for "all males" and "all females" but you do not see the means for "all tall subjects" and "all short subjects" which would have been produced had you specified independent variable Height as the first grouping variable rather than the second. Statistical Tests in Breakdowns. If you are interested in differences concerning the means, then the appropriate test is the breakdowns one-way ANOVA (F test).
If you are interested in variation differences, then you should test for homogeneity of variances. Other Related Data Analysis Techniques. Although for exploratory data analysis, breakdowns can use more than one independent variable, the statistical procedures in breakdowns assume the existence of a single grouping factor (even if, in fact, the breakdown results from a combination of a number of grouping variables).
Thus, those statistics do not reveal or even take into account any possible interactions between grouping variables in the design. For example, there could be differences between the influence of one independent variable on the dependent variable at different levels of another independent variable (e.
You can explore such effects by examining breakdowns "visually," using different orders of independent variables, but the magnitude or significance of such effects cannot be estimated by the breakdown statistics. Post-Hoc Comparisons of Means. Usually, after obtaining a statistically significant F test from the ANOVA, one wants to know which of the means contributed to the effect (i.Send me emails about new comments.
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Introduction to Linear Algebra, Fifth Edition (2016)
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