What is lower triangular matrix?

A lower triangular matrix is a square matrix in which all the entries above the main diagonal are zero. In other words, every element that is not on or below the main diagonal is zero.

For example, a 3x3 lower triangular matrix looks like this:

a 0 0
b c 0
d e f

Lower triangular matrices are commonly used in mathematical computations and computer programming for various applications, such as solving linear systems, calculating determinants, and performing matrix factorizations.

One of the main advantages of lower triangular matrices is that they are easier to work with computationally since many algorithms and operations can take advantage of the zero entries to simplify calculations.

In terms of storage, lower triangular matrices are more compact than general matrices, as only the non-zero elements need to be stored. This can be particularly useful when working with large matrices or when memory is limited.

Overall, lower triangular matrices are a useful mathematical concept with practical applications in various fields.