What is a Quasi Upper Triangular Matrix?

  • Thread starter jezza10181
  • Start date
  • Tags
    Matrix
In summary, a 'quasi upper triangular matrix' is a block upper triangular matrix with either 1x1 or 2x2 blocks on the diagonal. It is mentioned in the book 'Matrix Computations' by Golub & Van Loan, and although there is no formal definition available, it can be understood from the context in the book. There are also online resources, such as the first link provided, that provide further explanation and examples of this type of matrix.
  • #1
jezza10181
13
1
Hi, I am dealing with a 'quasi upper triangular matrix', that is mentioned in the book 'Matrix Computations' by Golub & Van Loan. However, neither in the book itself, or anywhere on the internet, am I able to find a formal definition of a 'quasi upper triangular matrix'.

I have a rough idea what this is.. an upper triangular matrix, with the odd non-zero element(s), somewhere along it's sub-diagonal. But I need an actual formal definition. Anyone furnish me with one please?
 
Physics news on Phys.org
  • #2
jezza10181 said:
I have a rough idea what this is.. an upper triangular matrix, with the odd non-zero element(s), somewhere along it's sub-diagonal. But I need an actual formal definition. Anyone furnish me with one please?

You probably mean "a block upper triangular matrix with either 1x1 or 2x2 blocks on the diagonal."

http://books.google.co.uk/books?id=...epage&q=quasi upper triangular matrix&f=false

http://reference.wolfram.com/legacy.../AdvancedDocumentationLinearAlgebra3.4.5.html

It should be clear exactly what G&VL mean from the context in the book.
 
  • #3
Thanks, the first link was very helpful
 

What is a Quasi Upper Triangular Matrix?

A Quasi Upper Triangular Matrix is a type of matrix where all the elements below the main diagonal are zero, and the elements on and above the main diagonal are either non-zero or zero. This matrix is also known as a subdiagonal matrix.

What are the properties of a Quasi Upper Triangular Matrix?

A Quasi Upper Triangular Matrix has the following properties:

  • It is a square matrix.
  • All elements below the main diagonal are zero.
  • The elements on and above the main diagonal can be either non-zero or zero.
  • The main diagonal can have both zero and non-zero elements.
  • The eigenvalues of a Quasi Upper Triangular Matrix are the elements on the main diagonal.

What is the difference between a Quasi Upper Triangular Matrix and an Upper Triangular Matrix?

The main difference between a Quasi Upper Triangular Matrix and an Upper Triangular Matrix is that in a Quasi Upper Triangular Matrix, the main diagonal can have both zero and non-zero elements, while in an Upper Triangular Matrix, all elements on the main diagonal are non-zero.

What are some applications of Quasi Upper Triangular Matrices?

Quasi Upper Triangular Matrices have various applications in mathematics, physics, and engineering. Some common applications include solving linear systems of equations, computing eigenvalues and eigenvectors, and representing networks and systems in control theory.

How is a Quasi Upper Triangular Matrix created?

A Quasi Upper Triangular Matrix can be created by selecting a square matrix and setting all the elements below the main diagonal to zero. The elements on and above the main diagonal can be chosen freely to create the desired matrix. Alternatively, a Quasi Upper Triangular Matrix can be obtained by applying row and column operations to a given matrix.

Similar threads

A Elementwise Derivative of a Matrix Exponential
    • Linear and Abstract Algebra
Replies
2
Views
2K
How do I check if a 1x1 matrix is diagonal, lower/upper triangular?
    • Linear and Abstract Algebra
Replies
2
Views
9K
LU decomposition of matrix
    • Linear and Abstract Algebra
Replies
4
Views
2K
Operator in a real vector space has an upper block triangular matrix
    • Linear and Abstract Algebra
Replies
1
Views
2K
Finding determinant with upper triangular matrix
    • Linear and Abstract Algebra
Replies
6
Views
30K
Proving Triangular Matrix Inverse is Also Triangular
    • Linear and Abstract Algebra
Replies
1
Views
2K
What Changes in the Third Pivot When a3,3 Shifts from 7 to 11 in Linear Algebra?
    • Linear and Abstract Algebra
Replies
1
Views
1K
MHB What are the ideals of the matrix ring?
    • Linear and Abstract Algebra
Replies
6
Views
2K
Help Diagonal matrix similar to upper triangular matrix?
    • Linear and Abstract Algebra
Replies
2
Views
13K
Is the 0 matrix upper triangular?
    • Calculus and Beyond Homework Help
Replies
2
Views
4K

Hot Threads

Recent Insights

Back
Top