Cramer's rule is an explicit formula in linear algebra for the solution of a system of linear equations that has as many equations as unknowns, valid whenever the system has a unique solution. It expresses each unknown through determinants: the determinant of the square coefficient matrix, and the determinant of a matrix obtained by replacing one column of the coefficient matrix with the column vector of right-hand sides. The rule is named after Gabriel Cramer, who published it for an arbitrary number of unknowns in 1750. Colin Maclaurin had published special cases in 1748 and possibly knew of the rule as early as 1729, so the naming reflects publication history rather than sole priority. The formula is valuable for theory and for small systems, giving each unknown as a ratio of two determinants.
Facts
Time Complexity
Time Complexity (category) Connections
Credited To
Source Cramer's rule (Wikipedia)
In Field
Source Cramer's rule (Wikipedia)
Invented
Source Cramer's rule (Wikipedia)
In the Other Atlases
Same As
Also in Mathematics Atlas: the same subject.
Sources
1. Cramer's rule (Wikipedia)
Practical Considerations [complexity-category]
In 1983, an algorithm for solving the system using Cramer's rule in
In Group: Linear Algebra and Matrix Decomposition, Lead paragraph
In linear algebra, Cramer's rule is an explicit formula
Invented: Gabriel Cramer, Lead paragraph
who published the rule for an arbitrary number of unknowns in 1750
Credited To: Gabriel Cramer, Lead paragraph [credited-to]
It is named after Gabriel Cramer
In Field: Algorithms and Complexity Theory, Practical Considerations
In 1997, an algorithm for solving a system using Cramer's rule with complexity equal to that of matrix multiplication was proposed.
View the SourceReader Challenges (0)
No disputes yet. Spotted an error or a better source? Open the first one.
Sign in to dispute this or suggest a correction.