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 of an orthonormal set of functions. The primary
applic
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.
Transformations and Relationships
between Variables
Outliers r
Matched pair design is when they explicitly divide subjects into groups of
TWO, applying a different treatment to one subject from each of the pairs they have divided.
Randomised Block Designs is when they divide them into TWO CATERGORIES (e.g. Male and F
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Recommended graphical tODIS
- if you want to summarise one variable
a and it is quantitative: a histogram or boxplot
- and it is categorical: a bar graph (or "bar chart) A
If
a If you want to explore the relationship between two variables
a and both are q
Extension Trigonometry
Compound Angles
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Marital Status
Never Married
Married
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Divorced
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Married
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Location
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Elsewhere (In Australia)
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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-squares approximate solutions and applications
to data-fi
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 that most of what we did in Rn and everything
weve done s
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 square matrix A is invertible if and only if its
determinant
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 any fixed directions? The discussion centers on the
eige
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 can be diagonalized and what the obstructions are
to thi
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
Example #1: Solve the system
.
5 x 3 y 9
This is easy to s
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 matrix, and how to find matrices for
several important g
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 and how to find an inverse matrix, and the
basic rules of
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 particular, well focus on the kernel and image of a linear
t
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 basis.
Coordinates relative to a basis
Perhaps the singl
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 same way in any space where we can add elements and scale
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 have a trailing semicolon.