# Textbook Notes for Mathematics at University of Toronto St. George (UTSG)

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UTSGMAT223H1Fabian ParschFall

## MAT223H1 Chapter Notes - Chapter 8.4: Diagonal Matrix, Symmetric Matrix, Asteroid Family

OC5374882 Page
5 Oct 2015
56
In this section we work on a very important factorization which is a generalization of the diagonalization procedure. This new approach is called the s
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UTSGMAT223H1Fabian ParschFall

## MAT223H1 Chapter Notes - Chapter 3.2: Matrix Addition, Diagonal Matrix, Block Matrix

OC5374885 Page
1 Oct 2015
38
In this section we study the algebra of matrices, that is the. Arithmetic operations that can be performed over matri- ces and their properties. Althou
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UTSGMAT223H1Fabian ParschFall

## MAT188H1 Chapter 2.2: Chapter 2.2 Span

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27 Sep 2015
34
The span of a set of vectors {u1, u2, . , um} is a subset of vector space de ned by all possible linear combinations of vectors from that set. The span
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UTSGMAT223H1Fabian ParschFall

## MAT223H1 Chapter Notes - Chapter 1.3: Roundoff, Pivot Element, Golu

OC5374882 Page
27 Sep 2015
27
Elimination methods work ne for small systems, but can lead to errors when implemented on computer system due to round-off errors. In addition, the num
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UTSGMAT223H1Fabian ParschFall

## MAT223H1 Chapter Notes - Chapter 1.1: The Algorithm

OC5374882 Page
27 Sep 2015
26
Introduction to linear equations: no solution is inconsistent. Trying to solve a1x1 + a2x2 = b1 a1x1 + a2x2 = b2 is inconsistent if b1 (cid:54)= b2. Be
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UTSGMAT223H1Fabian ParschFall

## MAT223H1 Chapter Notes - Chapter 6.1: Asteroid Family, Eigenvalues And Eigenvectors

OC5374882 Page
5 Oct 2015
26
Eigenvalues and eigenvectors are particular properties of matrices and linear transformations. They are important in many elds, such as nance, quan- tu
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UTSGMAT223H1Fabian ParschFall

## MAT188H1 Chapter 2.3: Chapter 2.3 Linear Independence

OC5374882 Page
27 Sep 2015
20
If the only solution to the vector equation x1u1 + x2u2 + . + xmum = 0 (1) is the trivial solution then the set x1 = x2 = . xm = 0, (cid:8)u1, . If the
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UTSGMAT223H1Fabian ParschFall

## MAT223H1 Chapter Notes - Chapter 3.1: Codomain

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1 Oct 2015
22
Linear transformations are a special type of function that appears in many practical elds such as nance, engineer- ing, social sciences, etc. T : rm rn
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UTSGMAT223H1Fabian ParschFall

## MAT223H1 Chapter Notes - Chapter 8.3: Triangular Matrix, Bmw 8 Series, Diagonal Matrix

OC5374881 Page
5 Oct 2015
26
Lets remember that an n n matrix a. A = a12 a22 a32 a11 a13 a21 a23 a31 a33 an1 an2 an3 a1n a2n a3n ann is called symmetric if aij = aji (1) for all i,
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UTSGMAT223H1Fabian ParschFall

## MAT188H1 Chapter 5.3: Chapter 5.3 Applications of the Determinant

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2 Oct 2015
38
Let s be the unit square in the rst quadrant of r2, and consider a linear transformation t : r2 r2. Assume that such linear transformations is represen
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UTSGMAT223H1Fabian ParschFall

## MAT223H1 Chapter Notes - Chapter 1.2: Row Echelon Form, The Algorithm, Elementary Matrix

OC5374882 Page
27 Sep 2015
24
1 linear systems elementary opera- is equivalent to tions. We present a systematic approach for converting any lin- ear system into its echelon form. T
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UTSGMAT223H1Fabian ParschFall

## MAT223H1 Chapter Notes - Chapter 4.1: Scalar Multiplication, Mull, Root Mean Square

OC5374882 Page
1 Oct 2015
25
Subspaces are special subsets of a vector space (rn in our case) that are connected to spanning sets, linear transfor- mations, and systems of linear e
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