“Fundamental matrix (linear differential equation)”的意思、由来-开放百科全书

词条

Fundamental matrix (linear differential equation)

释义

Control theory
References
See also

{{dablink|For other senses of the term, see Fundamental matrix (disambiguation).}}

In mathematics, a fundamental matrix of a system of n homogeneous linear ordinary differential equations

is a matrix-valued function whose columns are linearly independent solutions of the system.

Then every solution to the system can be written as , for some constant vector (written as a column vector of height n).

One can show that a matrix-valued function is a fundamental matrix of if and only if and is a non-singular matrix for all .^[1]

Control theory

The fundamental matrix is used to express the state-transition matrix, an essential component in the solution of a system of linear ordinary differential equations.

References

1. ^{{cite book |author=Chi-Tsong Chen |year=1998 |title=Linear System Theory and Design |edition=3rd |publisher=Oxford University Press |location=New York |isbn=978-0195117776}}

Control theory

References

See also