Uncovering the Origins of the Secular Matrix: A Fascinating Exploration

  • Thread starter Entropia
  • Start date
  • Tags
    Matrix
In summary, the term "secular matrix" is a physics term that represents the evolution of an operator over time. Its origins can be traced back to the Latin word "saeculum" which means "a long period of time". It is also related to the concept of secular effects in astronomy, which refers to gradual changes that occur over time. The term "secular" also has a religious connotation, stemming from the division of topics into those that are heavenly and outside of time, and those that are bound to the flow of time.
  • #1
Entropia
1,474
1
does anybody know the origins behind the *name* secular matrix?

i don't understand why a secular matrix would be called... secular.
 
Physics news on Phys.org
  • #2
First, the term "secular" matrix is not a mathematical term- it is a physics term. If you look up the word "secular" in a dictionary, you will find that one of its meanings has to do with time. The "secular matrix" in quantum physics is the matrix that represents the evolution of a an operator over time.
 
  • #3
Saeculum is the Latin noun meaning "a long period of time", sometimes interpreted in modern times as a century. Nominative plural saecula, plural genitive saeculorum (as in the great seal of the US: Novus ordo saeculorum = "A new order for the ages")

Secular effects in Astronomy are those that take place over a long time, gradually accumulating.

The other meaning of secular, "not religious", comes from the division in the middle ages of topics that were religious = heavenly = outside of time, versus the other kind that were bound to the flow of time found here below.
 

1. What is a secular matrix?

A secular matrix is a mathematical concept used in linear algebra. It refers to a square matrix that does not have any eigenvalues (or characteristic roots) that are complex numbers.

2. How is a secular matrix different from a non-secular matrix?

A non-secular matrix, also known as a non-normal matrix, can have complex eigenvalues. This means that it cannot be diagonalized or transformed into a simpler form. In contrast, a secular matrix can be transformed into a simpler form through diagonalization.

3. What are the applications of secular matrices in science?

Secular matrices are commonly used in quantum mechanics, specifically in the study of energy levels of physical systems. They are also used in control theory and signal processing to analyze and design complex systems.

4. How are secular matrices related to secularization?

The term "secular" in secular matrix refers to its mathematical definition of not having complex eigenvalues. It is not directly related to the concept of secularization, which refers to the declining influence of religion in society.

5. Can secular matrices only be used in specific fields of science?

No, secular matrices are a universal mathematical concept and can be applied in various fields of science, including physics, engineering, and economics. They are also used in computer science for data analysis and machine learning algorithms.

Similar threads

Replies
2
Views
2K
  • Linear and Abstract Algebra
Replies
2
Views
302
  • Linear and Abstract Algebra
Replies
1
Views
1K
  • Linear and Abstract Algebra
Replies
3
Views
1K
  • Linear and Abstract Algebra
Replies
3
Views
1K
  • Linear and Abstract Algebra
Replies
3
Views
1K
  • Linear and Abstract Algebra
Replies
3
Views
1K
  • Linear and Abstract Algebra
Replies
6
Views
1K
  • Linear and Abstract Algebra
Replies
8
Views
781
  • Linear and Abstract Algebra
Replies
5
Views
2K
Back
Top