Table of Contents
- 1 Which of the following matrix is both lower and upper triangular matrix?
- 2 How do you find the lower triangular matrix from the upper triangular matrix?
- 3 How do you find the lower triangular matrix?
- 4 Can upper and lower triangular matrices have the same product?
- 5 Why do we use triangular matrices in numerical analysis?
Which of the following matrix is both lower and upper triangular matrix?
Diagonal matrices
Diagonal matrices are both upper and lower triangular since they have zeroes above and below the main diagonal.
How do you find the lower triangular matrix from the upper triangular matrix?
Starts here5:22Chapter 04.01: Lesson: Upper and Lower Triangular Matrices – YouTubeYouTubeStart of suggested clipEnd of suggested clip59 second suggested clipSo again for determining whether a particular matrix is lower triangular you have to look at what isMoreSo again for determining whether a particular matrix is lower triangular you have to look at what is above the diagonal. And if all the elements above the diagonal are 0.
Which of the following is lower triangular matrix?
A triangular matrix is a special type of square matrix where all the values above or below the diagonal are zero. L is called a lower triangular matrix and U is called an upper triangular matrix.
Which of the following is an upper triangular matrix?
The upper triangular matrix has all the elements below the main diagonal as zero. Also, the matrix which has elements above the main diagonal as zero is called a lower triangular matrix….
| Related Links | |
|---|---|
| Types Of Matrices | Determinants and Matrices |
| Matrix Multiplication | Matrix Addition & Subtraction Of Two Matrices |
How do you find the lower triangular matrix?
The main diagonal is the set of entries that run from the upper left-hand corner of the matrix down to the lower right-hand corner of the matrix. Lower triangular matrices are matrices in which all entries above the main diagonal are 0.
Can upper and lower triangular matrices have the same product?
However, operations mixing upper and lower triangular matrices do not in general produce triangular matrices. For instance, the sum of an upper and a lower triangular matrix can be any matrix; the product of a lower triangular with an upper triangular matrix is not necessarily triangular either.
What is the definition of a strictly triangular matrix?
Strictly triangular matrix. If all of the entries on the main diagonal of a (upper or lower) triangular matrix are 0, the matrix is called strictly (upper or lower) triangular. All strictly triangular matrices are nilpotent, and the set of strictly upper (or lower) triangular matrices forms a nilpotent Lie algebra,…
What is the difference between triangular matrix and unitriangular matrix?
If the entries on the main diagonal of a (upper or lower) triangular matrix are all 1, the matrix is called (upper or lower) unitriangular. All unitriangular matrices are unipotent.
Why do we use triangular matrices in numerical analysis?
Because matrix equations with triangular matrices are easier to solve, they are very important in numerical analysis. By the LU decomposition algorithm, an invertible matrix may be written as the product of a lower triangular matrix L and an upper triangular matrix U if and only if all its leading principal minors are non-zero.