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

*label*Mathematics

*timer*Asked: Jan 21st, 2019

*account_balance_wallet*$15

### Question Description

Choose one of the following topics:

- Diagonalization Argument
- Continuum Hypothesis
- Power Sets
- 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

Attached.

Running Head: DIAGONALIZATION

1

Diagonalization

Institution Affiliation

Name

DIAGONALIZATION

2

Diagonalization

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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