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

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

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

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

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

View Document## MAT188H1 Chapter 2.2: Chapter 2.2 Span

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

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

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

View Document## MAT223H1 Chapter Notes - Chapter 1.1: The Algorithm

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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

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

26

Eigenvalues and eigenvectors are particular properties of matrices and linear transformations. They are important in many elds, such as nance, quan- tu

View Document## MAT188H1 Chapter 2.3: Chapter 2.3 Linear Independence

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

View Document## MAT223H1 Chapter Notes - Chapter 3.1: Codomain

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

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

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,

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

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

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

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

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

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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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