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Question: What does `_EnvLinalg95` do?

Question:What does `_EnvLinalg95` do?

sursumCorda 1229 Maple 2023
linearalgebra eigenvector
November 20 2023
1

Why does _EnvLinalg95 only affect LinearAlgebra:-Eigenvectors (and Student:-LinearAlgebra:-Eigenvectors) and not LinearAlgebra:-Eigenvalues and LinearAlgebra:-EigenConditionNumbers? 
 

> 

restart;
> 

m := <3 , 4 | 4 , 3>;

m := Matrix(2, 2, {(1, 1) = 3, (1, 2) = 4, (2, 1) = 4, (2, 2) = 3})

 (1)
> 

LinearAlgebra:-Eigenvalues(m);

Vector(2, {(1) = 7, (2) = -1})

 (2)
> 

LinearAlgebra:-Eigenvectors(m);

Vector(2, {(1) = -1, (2) = 7}), Matrix(2, 2, {(1, 1) = -1, (1, 2) = 1, (2, 1) = 1, (2, 2) = 1})

 (3)
> 

LinearAlgebra:-EigenConditionNumbers(m);

Vector(2, {(1) = 1.00000000000000, (2) = 1.00000000000000}), Vector(2, {(1) = 8., (2) = 8.})

 (4)
> 

_EnvLinalg95 := true:
> 

whattype(m);

Matrix

 (5)
> 

LinearAlgebra:-Eigenvalues(m);

Vector(2, {(1) = 7, (2) = -1})

 (6)
> 

LinearAlgebra:-Eigenvectors(m):

Error, (in Matrix) invalid input: `Matrix/MakeInit` expects its 1st argument, initializer, to be of type list(list), but received [proc (i, j) options operator, arrow; `if`(j = 1 and i <= 2, (Vector(2, {(1) = 1, (2) = 1}))[i], rhs(fill_opt)) end proc]

  
> 

LinearAlgebra:-EigenConditionNumbers(m);

Vector(2, {(1) = 1.00000000000000, (2) = 1.00000000000000}), Vector(2, {(1) = 8., (2) = 8.})

 (7)
> 

_EnvLinalg95 := false:
> 

LinearAlgebra:-Eigenvectors(m);

Vector(2, {(1) = -1, (2) = 7}), Matrix(2, 2, {(1, 1) = -1, (1, 2) = 1, (2, 1) = 1, (2, 2) = 1})

 (8)


 

Download _EnvLinalg95.mws

I have read the help page of Eigenvectors but couldn't find anything related.
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