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LinearAlgebra

  

Rank

  

compute the rank of a Matrix

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

Rank(A)

Parameters

A

-

Matrix

Description

• 

If A does not have a floating-point datatype, then the Rank(A) function computes the rank of A by performing Gaussian elimination on the rows of A.

  

The rank of Matrix A is the number of non-zero rows in the resulting Matrix.

• 

In the case that the Matrix A has a floating-point datatype, a singular value decomposition and analysis is performed.

• 

This function is part of the LinearAlgebra package, and so it can be used in the form Rank(..) only after executing the command with(LinearAlgebra). However, it can always be accessed through the long form of the command by using LinearAlgebra[Rank](..).

Examples

withLinearAlgebra:

AScalarMatrixn,3

An000n000n

(1)

RankA

3

(2)

B7,1,2|2,1,1|3,0,1|2,7,3

B−723211072−1−1−3

(3)

RankB

2

(4)

numelemsRowSpaceB

2

(5)

FMatrix15,13,825,25,13,1125,45,13,725,datatype=float8

F0.2000000000000000.3333333333333330.3200000000000000.4000000000000000.3333333333333330.4400000000000000.800000000000000−0.3333333333333330.280000000000000

(6)

RankF

2

(7)

eqsu3cosq5u5=0,cosq4u1+sinq4u2+u6+cosq5u4=0,cosq5sinq4u1+cosq5cosq4u2+sinq5u3=0,sinq5sinq4u1sinq5cosq4u2+cosq5u3u5=0:

A,vGenerateMatrixeqs,u1,u2,u3,u4,u5,u6

A,v0010cosq50cosq4sinq40cosq501cosq5sinq4cosq5cosq4sinq5000sinq4sinq5cosq4sinq5cosq50−10,0000

(8)

Normalizeresimplifye,trig

Normalizeresimplifye,trig

(9)

RankA

3

(10)

See Also

Matrix