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  1. Sep 2025
  2. math.libretexts.org math.libretexts.org
    11.1: Self-adjoint or hermitian operators
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    1. hyperthes_is 27 Sep 2025
      The uniqueness of T∗ is clear by the previous observation.

      $$ \begin{align} &{\langle T^w, v\rangle}&\ =~&\overline{\langle v,T^w\rangle}&~~~\text{(conjugate symmetry)}\ =~&\overline{\langle Tv,w\rangle}&~~~\text{(by definition)} \end{align} $$

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    math.libretexts.org/Bookshelves/Linear_Algebra/Book:_Linear_Algebra_(Schilling_Nachtergaele_and_Lankham)/11:_The_Spectral_Theorem_for_normal_linear_maps/11.01:_Self-adjoint_or_hermitian_operators
  3. Mar 2025
  4. stats.libretexts.org stats.libretexts.org
    10.4: The Least Squares Regression Line
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    stats.libretexts.org/Bookshelves/Introductory_Statistics/Introductory_Statistics_(Shafer_and_Zhang)/10:_Correlation_and_Regression/10.04:_The_Least_Squares_Regression_Line
  5. stats.libretexts.org stats.libretexts.org
    5.2: The Standard Normal Distribution
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    stats.libretexts.org/Bookshelves/Introductory_Statistics/Introductory_Statistics_(Shafer_and_Zhang)/05:_Continuous_Random_Variables/5.02:_The_Standard_Normal_Distribution
  6. math.libretexts.org math.libretexts.org
    7.5: Upper Triangular Matrices
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    math.libretexts.org/Bookshelves/Linear_Algebra/Book:_Linear_Algebra_(Schilling_Nachtergaele_and_Lankham)/07:_Eigenvalues_and_Eigenvectors/7.05:_Upper_Triangular_Matrices
  7. stats.libretexts.org stats.libretexts.org
    4.E: Discrete Random Variables (Exercises)
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    stats.libretexts.org/Bookshelves/Introductory_Statistics/Introductory_Statistics_(Shafer_and_Zhang)/04:_Discrete_Random_Variables/4.E:_Discrete_Random_Variables_(Exercises)
  8. stats.libretexts.org stats.libretexts.org
    4.2: Probability Distributions for Discrete Random Variables
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    stats.libretexts.org/Bookshelves/Introductory_Statistics/Introductory_Statistics_(Shafer_and_Zhang)/04:_Discrete_Random_Variables/4.02:_Probability_Distributions_for_Discrete_Random_Variables
  9. stats.libretexts.org stats.libretexts.org
    3.3: Conditional Probability and Independent Events
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    stats.libretexts.org/Bookshelves/Introductory_Statistics/Introductory_Statistics_(Shafer_and_Zhang)/03:_Basic_Concepts_of_Probability/3.03:_Conditional_Probability_and_Independent_Events