ADS_matrix.ipynb

Kernel: SageMath 10.4

Row Reduction

C = Matrix(QQ,[[1,1,1,1],[5,1,2,2]]);C
print '--------------------'
C.echelon_form()

--------------------

[  1   0 1/4 1/4]
[  0   1 3/4 3/4]

H=Matrix(Integers(2),[[1,1,0,0,1,1],[1,0,1,0,1,0],[1,0,1,1,0,1],[0,1,1,1,0,0]]);H
print '--------------------'
H.echelon_form()

H=Matrix(Integers(2),[[1,1,0,1,0,0,1],[1,0,1,0,1,0,0],[0,1,1,0,0,1,0]]);H
print '*****************'
H.echelon_form()

H2=Matrix(Integers(2),[[1,1,0,1,1,1],[1,0,1,1,0,0],[0,1,1,0,1,0]]);H2
print '*****************'
H2.echelon_form()

A=[[2,1,0,4],[-1,2,1,0],[0,-1,2,1]]
A

matrix(A)

%html
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var (' D, P')
A = Matrix (QQ, [[4, 1, 0], [1, 5, 1], [0, 1, 4]]);A

(D,P)=A.right_eigenmatrix();(D,P)

P.inverse()*A*P

A2=Matrix(QQ,[[8,1,0],[1,5,1],[0,1,7]])

P=A2.right_eigenmatrix()[1]
P.numerical_approx(digits=3)
print '------------------'
D=(P.inverse()*A2*P);D.numerical_approx(digits=3)

A=Matrix(QQ,[[1, 0, 0],[0,2,1],[1,-1,4]])
A.right_eigenmatrix()

A=Matrix(QQ,[[2,1],[2,3]])
A.exp()

Matrix?

def inner(g,v,w,h):
    hs=[]
    for i in srange(len(v)):
        hs=hs+[g(v[i],w[i])]
    return g(hs)
        

srange(len([1,2,4]))

[0, 1, 2]

var('f','h')
inner(g=f,[1,2,3],[3,4,5],h=h)

  File "<ipython-input-11-b850776b61a4>", line 2
    inner(g=f,[Integer(1),Integer(2),Integer(3)],[Integer(3),Integer(4),Integer(5)],h=h)
                                                                                       ^
SyntaxError: positional argument follows keyword argument