Math S-21b Lecture #10 Notes
In todays lecture we finished up a few details on Least Square Approximate Solutions (see Lecture #9 notes),
and then reviewed inner product spaces and introduced the idea
Descriptive Statistics
Measures of location tell us how large (or small) the typical value is.
The mean also has a physical interpretation as the centre of gravity.
Median is the middle value.
Transfo
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TWO, applying a different treatment to one subject from each of the pairs they have divided.
Randomised Block Designs is when
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- and it is categorical: a bar graph (or "bar chart) A
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Extension Trigonometry
Compound Angles
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Marital Status
Never Married
Married
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Divorced
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Math S-21b Lecture #9 Notes
The main topics in this lecture are orthogonal projection, the Gram-Schmidt orthogonalization process, QR
factorization, isometries and orthogonal transformations, least-sq
Math S-21b Lecture #7-8 Notes
We now take up in greater detail the ideas of inner products and orthogonality beyond the more basic
constructions introduced earlier in the course. It should be noted th
Math S-21b Lecture #11 Notes
This week is all about determinants. Well discuss how to define them, how to calculate them, learn the allimportant property known as multilinearity, and show that a squar
Math S-21b Lecture #12 Notes
Todays lecture focuses on what might be called the structural analysis of linear transformations. What are
the intrinsic properties of a linear transformation? Are there a
Math S-21b Lecture #13 Notes
We continue with the discussion of eigenvalues, eigenvectors, and diagonalizability of matrices. We want to
know, in particular what conditions will assure that a matrix c
Math S-21b Lecture #1 Notes
The primary focus of this lecture is a systematic way of solving and understanding systems of linear equations
algebraically, geometrically, and logically.
x 4 y 11
Examp
Math S-21b Lecture #2 Notes
Todays lecture focuses on the vector and matrix formulations for a system of linear equations, linear
transformations defined by matrices, the meaning of the columns of a m
Math S-21b Lecture #3 Notes
Todays lecture features a continuation of geometrically-defined linear transformations specifically
projections and reflections, conditions for invertibility of a matrix an
Math S-21b Lecture #4 Notes
In this lecture we define and study subspaces of Rn, the span of a collection of vectors, and what it means for a
collection of vectors to be linearly independent. In parti
Math S-21b Lecture #5 Notes
Todays main topics are coordinates of a vector relative to a basis for a subspace and, once we understand
coordinates, the matrix of a linear transformation relative to a b
Math S-21b Lecture #6 -7 Notes
General Linear Spaces (Vector Spaces)
Though we have dealt exclusively so far with Rn and its subspaces, almost everything that we have developed
so far will work the sa
Tip: use "restart;" at the beginning of each question
When you start work on a new question, use the "restart;" command to clear
Maple's memory.
A warning message appears if the statement does not hav