The matrixGaussianSubstitute function returns the M coefficient number vector from a triangulated array representing the solution of a triangulated system of M simultaneous linear equations in M variables.

The input argument {NumMatrix} must be an M by M+1 matrix representing the original independent variable observations with the dependent variable in the last column all having been triangulated via the Gaussian elimination in the form of::

x x x x... x y

0 x x x... x y

0 0 x x... x y


0 0 0 0... x y

The output will be the M coefficient number vector representing the solution to the original system of M simultaneous equations in M unknowns.


The matrixGaussianSubstitute function is a non-destructive function useful when you want to solve a system of M simultaneous equations in M variables from a triangulated matrix. See Sedgewick[2] chap 37.




(matrixGaussianSubstitute NumMatrix)

Arguments Name Type Description
Argument:NumMatrixNumMatrix Matrix containing the triangulated original independent and dependent observations


A new number Vector containing the M coefficients of the solution.



Here are a number of links to Lambda coding examples which contain this instruction in various use cases.


Argument Types

Here are the links to the data types of the function arguments.


Here are also a number of links to functions having arguments with any of these data types.

append binaryInsert boolean cdr
compareEQ compareLE compareLT compareNE
compare cons copy delete
dimension display insert inside
integer isAtom isBitVector isBoolean
isByteVector isChar isCharacter isComplex
isDate isDictionary isDirectory isEqual
isError isFloatVector isIdentical isInside
isIntegerVector isInteger isLambda isMatrix
isMember isMoney isNumberMatrix isNumberVector
isNumber isObjectVector isObject isPair
isPcodeVector isString isStructure isSymbol
isText isType isVector length
list macroReplace makeGaussianMatrix makeGramMatrix
makeQuotedList map mapc matrixGaussianEliminate
matrixGaussianSubstitute member money new
number offset pair parent
parse pointer ref remove
resize reverse saveObject setCar
setCdr setLastCdr setq sizeof
sort string type uniqueInsert
vectorFill writelg writeln

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