Gaussian elimination
Systematic row operations
Gaussian elimination is a method for solving systems of linear equations by systematically transforming a matrix into row echelon form.
Named for mathematician Carl Friedrich Gauss, the technique uses elementary row operations—swapping rows, multiplying by constants, adding rows together—to isolate variables one by one.
It's foundational in linear algebra and computational mathematics.
Rotating around fixed point
- substitutionExchange of one for another
- systematicFollowing ordered procedures
- step-by-stepIn sequential stages
- algorithmicFollowing programmed steps
No vector redundant
Side-by-side sequences
- columnsUpright structural shafts
- rankPosition in hierarchy
- singularOne in number
- non-singularDenoting more than one
Algebraic statements without powers
- system of equationsMultiple equations sharing variables
- simultaneous equationsInterdependent mathematical relationships solved jointly
- consistentNot varying or contradicting
- inconsistentLacking steady uniformity
homogeneous · nonhomogeneous · overdetermined · underdetermined · no solution · dependent variable · independent variable · solvable
Bad-tempered, irritable
- well-conditionedIn peak physical state
- MATLABMatrix-focused computing platform
pivoting
Rotating around fixed point
- substitutionExchange of one for another
- systematicFollowing ordered procedures
- step-by-stepIn sequential stages
linear independence
No vector redundant
rows
Side-by-side sequences
linear equations
Algebraic statements without powers
- system of equationsMultiple equations sharing variables
- simultaneous equationsInterdependent mathematical relationships solved jointly
- consistentNot varying or contradicting
inconsistent · homogeneous · nonhomogeneous · overdetermined · underdetermined · no solution · dependent variable · independent variable · solvable · indeterminate
ill-conditioned
Bad-tempered, irritable
- well-conditionedIn peak physical state
- MATLABMatrix-focused computing platform
- linear algebramatrix, linear equation, vectors, linear function, matrices
- algorithmsalgorithm, algorithms, DFS, binary search, A star
- Gaussnormal distribution, bell curve, Gaussian curvature, degaussing
- numerical methodsbisection, interpolation, least squares, convergence, approximation
- algebravariables, equations, equation, polynomials, algebraic equations
- matricestranspose, determinants, rows, cells, Hermitian matrices