wdlang said:i have a 1000 by 1000 matrix A
A is definitely singular
I want to solve the null vector numerically
How to do this?
matlab does not work!
jbunniii said:Can you clarify what you mean by "solve the null vector"? Do you mean that you want to find a vector [tex]x \neq 0[/tex] such that [tex]Ax = 0[/tex]? i.e., to find a nonzero element of the null space?
wdlang said:yes!
The null vector, also known as the zero vector, is a vector with a magnitude of 0 and no specific direction. In other words, it has no components and is often represented as the origin (0,0) in a coordinate system.
Numerically solving the null vector is important because it allows us to find the values or parameters that make a system or equation equal to 0. This can help us solve equations, find solutions to problems, and understand physical phenomena.
There are several methods that can be used to numerically solve the null vector, including Gaussian elimination, LU decomposition, and matrix inversion. These methods involve manipulating and solving systems of linear equations.
Yes, in some cases, the null vector can be solved analytically using mathematical techniques such as substitution or elimination. However, in more complex systems or equations, it may be necessary to use numerical methods to find the null vector.
The null vector is used in various scientific fields, including physics, engineering, and computer science. It can be used to analyze and solve complex systems and equations, as well as to understand the behavior of physical phenomena. It is also used in data analysis and computer simulations.