Chapter 4 Projections and Linear Transformations 1. Inconsistent Systems and Projection 2. Orthogonal Bases 3. Properties of Determinants 2. Complex Eigenvalues and Jordan Canonical Form 2.
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A semester, or a year, or a decade goes by, and the core concepts of linear algebra tend to be forgotten in a way that basic algebra, geometry, and even calculus are not.
Concepts like rate of change, tangent line, slope, and area under a curve are fairly easily retained, even when specific formulas are not. Linear algebra is important in research, where we have several variables dimensions that describe observations, and we have predictions or comparisons to make in that multi-dimensional reality.
In 2-dimensional space, we may do something like map weight as a function of height, so that height is represented by the x-axis, and weight on the y-axis. We intuitively know how to find the distance between two points in this space — we use the Pythagorean theorem to figure it out.
If we imagined that we have the true height and weight of a given elephant plotted as a dot on the cartesian plane, and we had various guesses about its height and weight plotted as well, we could easily figure out which guess was the closest by measuring distance — squaring the difference between the true and guessed height, and squaring it, adding the squared difference between the true and guessed weight maybe counting in thousands of kg , and taking the square root.
When we measure the root mean square error of a linear model, we take the distance between actual and predicted points the residuals , square them all, average those squared values for normalization, and take the square root.
We square them because we want to find distance. Consider, for example, the Etch A Sketch, a toy with two dials that allows you to draw. One dial goes left and right only.
With those two dials together, you can draw anything in the plane. Perpendicular angles are the simplest solution to drawing in 2 dimensions. Video just for fun, and to demonstrate that with two perpendicular vectors you can access span the entire plane. The task of recombining variables to come up with the best set of variables that are correlated to each other as little as possible is called Principle Components Analysis, or PCA.
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LINEAR ALGEBRA A GEOMETRIC APPROACH S.ESAN PDF DOWNLOAD
Fenririsar This is the first book to provide C program for gauss elimination s. We ship from India. This book provides a self-contained and accessible introduction to linear and multilinear algebra. The Bookshelf application offers access: Most schools will have calculus prerequisites for those who are seeking a degree in engineering. A Geometric Approach by S. Summary This is an undergraduate textbook suitable for linear algebra courses. A Geometric Approach has 1 available editions to buy at Alibris.
Linear Algebra, a Geometric Approach
Linear Algebra. A Geometric Approach
Download: LINEAR ALGEBRA : A GEOMETRIC APPROACH.pdf