chapter 2 matrices and linear transformations
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Chapter 2 Matrices and Linear Transformations. Addition, Scalar Multiplication, and Multiplication of Matrices. Figure 2.1 An arbitrary m X n matrix A. Figure 2.2 The elements of a square matrix A where the subscripts are equal, form the main diagonal. Figure 2.3. - PowerPoint PPT PresentationTRANSCRIPT
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Chapter 2
Matrices and Linear Transformations
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Addition, Scalar Multiplication, and Multiplication of Matrices
Figure 2.1 An arbitrary m X n matrix A.
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Figure 2.2 The elements of a square matrix A where the subscripts are equal, form the main diagonal.
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Figure 2.3
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Properties of Matrix Operations
Example 5
Figure 2.4
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Figure 2.5
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Example 6
Figure 2.6 Many networks are designed to accept signals at certain points and to deliver a modified version of the signals. Here, the usual arrangement is illustrated.
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Example 6 (cont’d)
Figure 2.7 An example of a two-port.
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Figure 2.8 Three two-ports with transmission matrices A, B, and C.
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Exercise Set 2.2
Figure 2.9 Determine the transmission matrices of the two-ports.
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Figure 2.10 A two-port that consists of three two-ports placed in series.
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Matrix Transformations, Rotations, and Dilations
Figure 2.11
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Figure 2.12
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Figure 2.13 Rotation about the origin.
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Figure 2.14 Matrix transformations.
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Example 1
Figure 2.15
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Figure 2.16
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Figure 2.17
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Theorem 2.9
Figure 2.18
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Figure 2.19
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Figure 2.20
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Linear Transformations, Graphics, and Fractals
Figure 2.21 Here, the structure preserving ideas of a linear transformation are illustrated.
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Figure 2.22
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Figure 2.23
Example 5
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Figure 2.24 Fractal pictures of nature.
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A Communication Model and Group Relationships in Sociology
Figure 2.25
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Figure 2.26
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Exercise Set 2.9
Figure 2.27
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Figure 2.28
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Figure 2.29
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Figure 2.30