Discussion: Diagonalization, Continuum Hypothesis, Power Sets, and Hilbert's Hotel Problem

timer Asked: Jan 21st, 2019
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Question Description

Choose one of the following topics:

  1. Diagonalization Argument
  2. Continuum Hypothesis
  3. Power Sets
  4. Hilbert’s Hotel Problem

Research your chosen topic further. After your research, reflect upon any unanswered questions, things you still want to know, or ideas about the concept you still find puzzling. This is not a summary. It is a reflection of your thoughts that were generated by this topic and by subsequent reading. It is a place to ask questions, speculate about answers, and share insights. If it is applicable to do so, it is highly recommended to include an attachment of custom or referenced illustrations to your thread to illustrate and support your ideas.

Tutor Answer

School: University of Virginia




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Diagonalizable matrix is those that are similar to the diagonal matrix, in most cases, such
are square matrices. The existence of an invertible matrix means that such a matrix can be
diagonalizable (Pollmann et al., 2016). In mathematical contexts, diagonalization is the process
of finding a diagonal matrix that corresponds with the linear map. It is intriguing to understand
that not all square matrix is diagonalizable (Jiang & Li, 2016). The most important aspect about
diagonalizable matrices is the interest they have as most if they are easy to handle especially
when their eigenvalues and eigenfactors are well known (Pollmann et al., 2016).
It is interesting to understand that one can easily raise a diagonal matrix to any power by
raising the diagonal entries to the same power, in this case, the determinant of the diagonal
matrix is usual...

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