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Problems in Analytic Geometry and Linear Algebra
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II · Linear Algebra
Chapter 14
Operators on Spaces with a Scalar Product
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14.1 · Operators on a Euclidean (Hermitian) Space
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14.2 · Operators on Pseudo-Euclidean, Hermitian, and Symplectic Spaces, and on Spaces with a General Scalar Product
Section 14.1
Operators on a Euclidean (Hermitian) Space
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Subsection 14.1.1
The Adjoint Operator
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Subsection 14.1.2
Self-Adjoint Operators
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Subsection 14.1.3
Skew-Symmetric and Skew-Hermitian Operators
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Subsection 14.1.4
Orthogonal and Unitary Operators. Transformation Groups
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Subsection 14.1.5
Polar Decomposition
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Subsection 14.1.6
Normal Operators
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Subsection 14.1.7
Operators on Euclidean Spaces and Systems of Linear Equations
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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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Subsection 14.2.1
Adjoint Operators
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Subsection 14.2.2
Operators Preserving the Scalar Product (Isometric Operators)
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Subsection 14.2.3
Self-Adjoint (Symmetric, Hermitian) and Skew-Symmetric (Skew-Hermitian) Operators
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