matrixGaussianEliminate

 

 

Description

The matrixGaussianEliminate function triangulates the M by M+1 coefficient matrix representing a system of M simultaneous linear equations in M variables.

The input argument {NumMatrix} must be an M by M+1 number matrix representing the original independent variable observations with the dependent variable in the last column in the form of:

x x x x... y

x x x x... y

....

x x x x... y

The output will be the M by M+1 matrix after triangulation. The triangulated result matrix is now ready for Gaussian substitution.

When to use

The matrixGaussianEliminate function is a non-destructive function useful when you want to create a triangulated Gaussian matrix in preparation for primal form regression. See Sedgewick[2] chap 37.

 

Syntax

(matrixGaussianEliminate NumMatrix)

Name Description AIS Types
NumMatrix Matrix containing the original independent and dependent observationsNumMatrix

Returns:

A new triangulated number Matrix object after Gaussian elimination.

 

Examples

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

Example_NumMatrix_matrixGaussianEliminate_001

This example triangulates a Number Matrix to its Gaussian Matrix.

 

Argument Types

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

NumMatrix

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

binaryInsert(CpxVector) binaryInsert(FltVector) binaryInsert(IntVector) binaryInsert(Matrix)
binaryInsert(NumMatrix) binaryInsert(NumVector) binaryInsert(ShortVector) binaryInsert(Structure)
binaryInsert(Vector) boolean(Boolean) cdr(BitVector) cdr(Brick)
cdr(CpxVector) cdr(Dictionary) cdr(Directory) cdr(FltVector)
cdr(IntVector) cdr(List) cdr(Matrix) cdr(NumMatrix)
cdr(NumVector) cdr(ObjVector) cdr(ShortVector) cdr(Structure)
cdr(Vector) character(Character) compareEQ(BitVector) compareEQ(Boolean)
compareEQ(Brick) compareEQ(Character) compareEQ(Complex) compareEQ(CpxVector)
compareEQ(Date) compareEQ(Dictionary) compareEQ(Directory) compareEQ(FltVector)
compareEQ(Function) compareEQ(IntVector) compareEQ(Lambda) compareEQ(List)
compareEQ(Matrix) compareEQ(NumMatrix) compareEQ(NumVector) compareEQ(Number)
compareEQ(ObjVector) compareEQ(ObjectRepository) compareEQ(Pair) compareEQ(ShortVector)
compareEQ(String) compareEQ(Structure) compareEQ(Symbol) compareEQ(Vector)
compareEQ(Void) compareLE(BitVector) compareLE(Boolean) compareLE(Brick)
compareLE(Character) compareLE(Complex) compareLE(CpxVector) compareLE(Date)
compareLE(Dictionary) compareLE(Directory) compareLE(FltVector) compareLE(Function)
compareLE(IntVector) compareLE(Lambda) compareLE(List) compareLE(Matrix)
compareLE(NumMatrix) compareLE(NumVector) compareLE(Number) compareLE(ObjVector)
compareLE(ObjectRepository) compareLE(Pair) compareLE(ShortVector) compareLE(String)
compareLE(Structure) compareLE(Symbol) compareLE(Vector) compareLE(Void)
compareLT(BitVector) compareLT(Boolean) compareLT(Brick) compareLT(Character)
compareLT(Complex) compareLT(CpxVector) compareLT(Date) compareLT(Dictionary)
compareLT(Directory) compareLT(FltVector) compareLT(Function) compareLT(IntVector)
compareLT(Lambda) compareLT(List) compareLT(Matrix) compareLT(NumMatrix)
compareLT(NumVector) compareLT(Number) compareLT(ObjVector) compareLT(ObjectRepository)
compareLT(Pair) compareLT(ShortVector) compareLT(String) compareLT(Structure)
compareLT(Symbol) compareLT(Vector) compareLT(Void) compareNE(BitVector)
compareNE(Boolean) compareNE(Brick) compareNE(Character) compareNE(Complex)
compareNE(CpxVector) compareNE(Date) compareNE(Dictionary) compareNE(Directory)
compareNE(FltVector) compareNE(Function) compareNE(IntVector) compareNE(Lambda)
compareNE(List) compareNE(Matrix) compareNE(NumMatrix) compareNE(NumVector)
compareNE(Number) compareNE(ObjVector) compareNE(ObjectRepository) compareNE(Pair)
compareNE(ShortVector) compareNE(String) compareNE(Structure) compareNE(Symbol)
compareNE(Vector) compareNE(Void) compare(BitVector) compare(Boolean)
compare(Brick) compare(Character) compare(Complex) compare(CpxVector)
compare(Date) compare(Dictionary) compare(Directory) compare(FltVector)
compare(Function) compare(IntVector) compare(Lambda) compare(List)
compare(Matrix) compare(NumMatrix) compare(NumVector) compare(Number)
compare(ObjVector) compare(ObjectRepository) compare(Pair) compare(ShortVector)
compare(String) compare(Structure) compare(Symbol) compare(Vector)
compare(Void) cons(Pair) copy(BitVector) copy(Brick)
copy(CpxVector) copy(Dictionary) copy(Directory) copy(FltVector)
copy(IntVector) copy(Lambda) copy(List) copy(Matrix)
copy(NumMatrix) copy(NumVector) copy(ObjVector) copy(Pair)
copy(PcodeVector) copy(ShortVector) copy(Structure) copy(Vector)
delete(Dictionary) delete(Directory) delete(FltVector) delete(IntVector)
delete(List) delete(Matrix) delete(NumMatrix) delete(NumVector)
delete(ObjVector) delete(ObjectRepository) delete(Pair) delete(ShortVector)
delete(Structure) delete(Vector) display(ByteVector) display(FileIO)
insert(Dictionary) insert(Directory) insert(FltVector) insert(IntVector)
insert(Matrix) insert(NumMatrix) insert(NumVector) insert(ObjVector)
insert(ShortVector) insert(Structure) insert(Vector) inside(BitVector)
inside(Dictionary) inside(Directory) inside(IntVector) inside(List)
inside(Matrix) inside(NumMatrix) inside(NumVector) inside(ShortVector)
inside(Structure) inside(Vector) integer(Integer) isAtom(BitVector)
isAtom(Brick) isAtom(Dictionary) isAtom(Directory) isAtom(FltVector)
isAtom(IntVector) isAtom(List) isAtom(Matrix) isAtom(NumMatrix)
isAtom(NumVector) isAtom(ObjVector) isAtom(Pair) isAtom(PcodeVector)
isAtom(ShortVector) isAtom(Structure) isAtom(Vector) isBitVector(BitVector)
isBoolean(Boolean) isByteVector(ByteVector) isChar(String) isCharacter(Character)
isComplex(Complex) isDate(Date) isDictionary(Dictionary) isDirectory(Directory)
isEqual(BitVector) isEqual(Boolean) isEqual(Brick) isEqual(Character)
isEqual(Complex) isEqual(Date) isEqual(Dictionary) isEqual(Directory)
isEqual(FltVector) isEqual(Function) isEqual(IntVector) isEqual(List)
isEqual(Matrix) isEqual(NumMatrix) isEqual(NumVector) isEqual(Number)
isEqual(ObjVector) isEqual(Pair) isEqual(ShortVector) isEqual(String)
isEqual(Structure) isEqual(Vector) isEqual(Void) isError(Error)
isFloatVector(FltVector) isIdentical(BitVector) isIdentical(Boolean) isIdentical(Brick)
isIdentical(Character) isIdentical(Complex) isIdentical(Date) isIdentical(Dictionary)
isIdentical(Directory) isIdentical(Error) isIdentical(FltVector) isIdentical(Function)
isIdentical(IntVector) isIdentical(List) isIdentical(Matrix) isIdentical(NumMatrix)
isIdentical(NumVector) isIdentical(Number) isIdentical(ObjVector) isIdentical(ObjectRepository)
isIdentical(Pair) isIdentical(PcodeVector) isIdentical(ShortVector) isIdentical(Structure)
isIdentical(Vector) isIdentical(Void) isInside(BitVector) isInside(Dictionary)
isInside(Directory) isInside(IntVector) isInside(List) isInside(Matrix)
isInside(NumMatrix) isInside(NumVector) isInside(ObjVector) isInside(Pair)
isInside(ShortVector) isInside(Structure) isInside(Vector) isIntegerVector(IntVector)
isInteger(Integer) isMatrix(Matrix) isMember(BitVector) isMember(Dictionary)
isMember(Directory) isMember(IntVector) isMember(List) isMember(Matrix)
isMember(NumMatrix) isMember(NumVector) isMember(ObjVector) isMember(Pair)
isMember(ShortVector) isMember(Structure) isMember(Vector) isMoney(Number)
isNumberMatrix(NumMatrix) isNumberVector(NumVector) isNumber(Number) isObjectVector(ObjVector)
isObject(BitVector) isObject(Brick) isObject(ByteVector) isObject(Dictionary)
isObject(Directory) isObject(FltVector) isObject(IntVector) isObject(List)
isObject(Matrix) isObject(NumMatrix) isObject(NumVector) isObject(ObjVector)
isObject(Pair) isObject(PcodeVector) isObject(ShortVector) isObject(String)
isObject(Structure) isObject(Symbol) isObject(Vector) isPair(List)
isPair(Pair) isPcodeVector(PcodeVector) isString(String) isStructure(Structure)
isSymbol(Symbol) isText(String) isType(BitVector) isType(Boolean)
isType(Brick) isType(Character) isType(Complex) isType(Date)
isType(Dictionary) isType(Directory) isType(FltVector) isType(Function)
isType(IntVector) isType(Matrix) isType(NumMatrix) isType(NumVector)
isType(Number) isType(ObjVector) isType(ObjectRepository) isType(Pair)
isType(ShortVector) isType(String) isType(Structure) isType(Symbol)
isType(Vector) isType(Void) isVector(Vector) length(BitVector)
length(Brick) length(Dictionary) length(Directory) length(FltVector)
length(IntVector) length(List) length(Matrix) length(NumMatrix)
length(NumVector) length(ObjVector) length(ObjectRepository) length(Pair)
length(PcodeVector) length(ShortVector) length(String) length(Structure)
length(Symbol) length(Vector) list(List) macroReplace(String)
makeGaussianMatrix(NumMatrix) makeGramMatrix(NumMatrix) makeQuotedList(List) map(Dictionary)
map(Directory) map(FltVector) map(IntVector) map(List)
map(Matrix) map(NumMatrix) map(NumVector) map(Pair)
map(ShortVector) map(Structure) map(Vector) mapc(Dictionary)
mapc(Directory) mapc(FltVector) mapc(IntVector) mapc(List)
mapc(Matrix) mapc(NumMatrix) mapc(NumVector) mapc(Pair)
mapc(ShortVector) mapc(Structure) mapc(Vector) matrixGaussianEliminate(NumMatrix)
matrixGaussianSubstitute(NumMatrix) member(BitVector) member(Dictionary) member(Directory)
member(IntVector) member(List) member(Matrix) member(NumMatrix)
member(NumVector) member(ObjVector) member(ShortVector) member(Structure)
member(Vector) money(Number) new(BitVector) new(Brick)
new(ByteVector) new(CpxVector) new(Dictionary) new(Directory)
new(FltVector) new(IntVector) new(Lambda) new(Matrix)
new(NumMatrix) new(NumVector) new(ObjVector) new(ObjectRepository)
new(PcodeVector) new(ShortVector) new(String) new(Structure)
new(Symbol) new(Vector) number(Number) pair(Pair)
parse(String) ref(BitVector) ref(Boolean) ref(Brick)
ref(Character) ref(Complex) ref(Date) ref(Dictionary)
ref(Directory) ref(FltVector) ref(Function) ref(IntVector)
ref(Lambda) ref(List) ref(Matrix) ref(NumMatrix)
ref(NumVector) ref(Number) ref(ObjVector) ref(ObjectRepository)
ref(PcodeVector) ref(ShortVector) ref(String) ref(Structure)
ref(Symbol) ref(Vector) ref(Void) remove(BitVector)
remove(Dictionary) remove(Directory) remove(IntVector) remove(Matrix)
remove(NumMatrix) remove(NumVector) remove(ObjVector) remove(ShortVector)
remove(Structure) remove(Vector) resize(BitVector) resize(Dictionary)
resize(Directory) resize(FltVector) resize(IntVector) resize(Matrix)
resize(NumMatrix) resize(NumVector) resize(ObjVector) resize(ShortVector)
resize(Structure) resize(Vector) reverse(BitVector) reverse(FltVector)
reverse(IntVector) reverse(List) reverse(Matrix) reverse(NumMatrix)
reverse(NumVector) reverse(ObjVector) reverse(ShortVector) reverse(Vector)
saveObject(ByteVector) saveObject(Integer) send(BitVector) send(Boolean)
send(Brick) send(Character) send(CpxVector) send(Date)
send(Dictionary) send(Directory) send(FltVector) send(Function)
send(IntVector) send(Lambda) send(List) send(Matrix)
send(NumMatrix) send(NumVector) send(Number) send(ObjectRepository)
send(Pair) send(ShortVector) send(String) send(Structure)
send(Symbol) send(Vector) send(Void) setCar(List)
setCar(Pair) setCdr(BitVector) setCdr(Brick) setCdr(Dictionary)
setCdr(Directory) setCdr(FltVector) setCdr(IntVector) setCdr(List)
setCdr(Matrix) setCdr(NumMatrix) setCdr(NumVector) setCdr(ObjVector)
setCdr(Pair) setCdr(ShortVector) setCdr(Structure) setCdr(Vector)
setLastCdr(BitVector) setLastCdr(FltVector) setLastCdr(IntVector) setLastCdr(List)
setLastCdr(Matrix) setLastCdr(NumMatrix) setLastCdr(NumVector) setLastCdr(ObjVector)
setLastCdr(Structure) setLastCdr(Vector) setq(BitVector) setq(Boolean)
setq(Brick) setq(Character) setq(Date) setq(Dictionary)
setq(Directory) setq(FltVector) setq(IntVector) setq(Lambda)
setq(List) setq(Matrix) setq(NumVector) setq(Number)
setq(ObjVector) setq(ObjectRepository) setq(PcodeVector) setq(ShortVector)
setq(String) setq(Structure) setq(Symbol) setq(Vector)
setq(Void) sizeof(BitVector) sizeof(Boolean) sizeof(Brick)
sizeof(ByteVector) sizeof(Character) sizeof(Complex) sizeof(Date)
sizeof(Dictionary) sizeof(Directory) sizeof(FltVector) sizeof(Function)
sizeof(IntVector) sizeof(List) sizeof(Matrix) sizeof(NumMatrix)
sizeof(NumVector) sizeof(Number) sizeof(ObjVector) sizeof(ObjectRepository)
sizeof(Pair) sizeof(PcodeVector) sizeof(ShortVector) sizeof(String)
sizeof(Structure) sizeof(Symbol) sizeof(Vector) sizeof(Void)
sort(BitVector) sort(Dictionary) sort(Directory) sort(FltVector)
sort(IntVector) sort(List) sort(Matrix) sort(NumMatrix)
sort(NumVector) sort(ObjVector) sort(ShortVector) sort(Structure)
sort(Vector) string(Complex) string(String) type(BitVector)
type(Boolean) type(Brick) type(ByteVector) type(Character)
type(Complex) type(Date) type(Dictionary) type(Directory)
type(FltVector) type(Function) type(IntVector) type(Lambda)
type(Matrix) type(NumMatrix) type(NumVector) type(Number)
type(ObjVector) type(ObjectRepository) type(Pair) type(PcodeVector)
type(ShortVector) type(String) type(Structure) type(Symbol)
type(Vector) type(Void) uniqueInsert(FltVector) uniqueInsert(IntVector)
uniqueInsert(Matrix) uniqueInsert(NumMatrix) uniqueInsert(NumVector) uniqueInsert(ObjVector)
uniqueInsert(ShortVector) uniqueInsert(Structure) uniqueInsert(Vector) vectorFill(BitVector)
vectorFill(FltVector) vectorFill(IntVector) vectorFill(Matrix) vectorFill(NumMatrix)
vectorFill(NumVector) vectorFill(ObjVector) vectorFill(ShortVector) vectorFill(Vector)
writeln(ByteVector) writeln(String) writeln(Text)

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