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Problems in Analytic Geometry and Linear Algebra
Part II
Linear Algebra
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789
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52%
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On this page
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10 · Basic Concepts of Linear Algebra
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11 · Operators on Linear Spaces
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12 · Bilinear and Quadratic Functions
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13 · Spaces with a Scalar Product
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14 · Operators on Spaces with a Scalar Product
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15 · Quadratic Functions and Second-Order Surfaces
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16 · Tensors
Chapter 10
Basic Concepts of Linear Algebra
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105
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60%
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Section 10.1
Vector Spaces, Linear Independence
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22
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41%
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Section 10.2
Basis, Dimension, Coordinates
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18
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100%
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Section 10.3
Linear Subspaces and Operations on Them
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22
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73%
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Section 10.4
Linear Functions and Mappings
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26
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42%
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Section 10.5
Affine Spaces
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17
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53%
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Chapter 11
Operators on Linear Spaces
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121
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52%
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Section 11.1
The Matrix of a Linear Operator
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18
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83%
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Section 11.2
Kernel and Image of a Linear Operator. Invariant Subspaces. Projectors. Complexification and Realification
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19
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21%
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Section 11.3
Substituting a Linear Operator into a Polynomial. Annihilating Polynomials
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19
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32%
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Section 11.4
Eigenvalues, Eigenvectors
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33
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45%
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Section 11.5
Jordan Normal Form of Linear Operators
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14
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64%
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Section 11.6
Substituting an Operator (Matrix) into a Function of a Numerical Argument
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12
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67%
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Section 11.7
Finding Invariant Subspaces
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6
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100%
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Chapter 12
Bilinear and Quadratic Functions
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49
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37%
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Section 12.1
General Facts about Bilinear and Sesquilinear Functions
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8
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25%
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Section 12.2
Symmetric and Skew-Symmetric, Hermitian and Skew-Hermitian Functions
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30
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27%
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Section 12.3
Reduction to Canonical Form
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11
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73%
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Chapter 13
Spaces with a Scalar Product
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140
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66%
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Section 13.1
Elementary Properties of the Scalar Product
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20
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60%
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Section 13.2
Orthogonal Systems of Vectors
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27
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70%
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Section 13.3
The Gram Matrix.
n
n
n
-Dimensional Volume
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28
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46%
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Section 13.4
Orthogonal Complement
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10
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80%
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Section 13.5
Distances and Angles
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12
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67%
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Section 13.6
Geometry of Affine Euclidean Spaces
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18
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89%
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Section 13.7
The
n
n
n
-Dimensional Cube and the
n
n
n
-Dimensional Simplex
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12
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75%
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Section 13.8
The Least Squares Method and Interpolation of Functions
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13
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54%
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Chapter 14
Operators on Spaces with a Scalar Product
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252
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51%
]
Section 14.1
Operators on a Euclidean (Hermitian) Space
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201
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54%
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Section 14.2
Operators on Pseudo-Euclidean, Hermitian, and Symplectic Spaces, and on Spaces with a General Scalar Product
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51
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37%
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Chapter 15
Quadratic Functions and Second-Order Surfaces
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23
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57%
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Section 15.1
Quadratic Functions on a Euclidean Space
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16
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50%
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Section 15.2
Second-Order Surfaces
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7
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71%
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Chapter 16
Tensors
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99
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33%
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Section 16.1
Basic Concepts
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19
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63%
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Section 16.2
Tensor Products of Spaces
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22
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27%
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Section 16.3
Symmetric and Skew-Symmetric Tensors
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31
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23%
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Section 16.4
Tensors on Euclidean and Symplectic Spaces
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20
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25%
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Section 16.5
The Hodge Operation and Euclidean Structure
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7
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43%
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