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# Edit detail for SandBox Matrix revision 6 of 6

 1 2 3 4 5 6 Editor: test1 Time: 2015/06/05 14:39:23 GMT+0 Note:

removed:
-
-From jcv Sat Oct 9 16:10:48 -0700 2010
-From: jcv
-Date: Sat, 09 Oct 2010 16:10:48 -0700
-Subject: test
-Message-ID: <20101009161048-0700@axiom-wiki.newsynthesis.org>
-
-M := matrix [[1,1,1,1],[a,a,b,b],[1,1,1,1],[a,a,b,b]]


Symbolic Matrices

fricas
A:=matrix [[x,y],[z,w]]
 (1)
Type: Matrix(Polynomial(Integer))
fricas
A+1
 (2)
Type: SquareMatrix?(2,Polynomial(Integer))

fricas
A+2
 (3)
Type: SquareMatrix?(2,Polynomial(Integer))

## Use the Edit and Preview Functions

Hey, why not learn to use the edit function instead of entering such a large number of similar comments?

Look at the top right hand side of the page.

fricas
N:=matrix[[0],[0]]
 (4)
Type: Matrix(NonNegativeInteger?)
fricas
L:=[[sqrt(-1)*sin(x)+cos(x)],[-sqrt(-1)*sin(x)+cos(x)]]
 (5)
Type: List(List(Expression(Integer)))
fricas
A:=matrix[[cos(x),-sin(x)],[sin(x),cos(x)]]
 (6)
Type: Matrix(Expression(Integer))
fricas
v:=matrix[[v11],[v12]]
 (7)
Type: Matrix(Polynomial(Integer))
fricas
C:=A*v-L(1,1)*v
 (8)
Type: Matrix(Expression(Integer))
fricas
solve(C(1,1)=0,v11)
 (9)
Type: List(Equation(Expression(Integer)))
fricas
solve(C(2,1)=0,v12)
 (10)
Type: List(Equation(Expression(Integer)))
fricas
V:=matrix[[1/sqrt(-1),1],[1,-1/sqrt(-1)]]
 (11)
Type: Matrix(AlgebraicNumber?)
fricas
Z:=matrix[[V(2,2),-V(1,2)],[-V(2,1),V(1,1)]]
 (12)
Type: Matrix(AlgebraicNumber?)
fricas
W:=(V(1,1)*V(2,2) - V(1,2)*V(2,1))
 (13)
Type: AlgebraicNumber?

fricas
N:=matrix[[0],[0]]
 (14)
Type: Matrix(NonNegativeInteger?)
fricas
L:=[[sqrt(-1)*sin(x)+cos(x)],[-sqrt(-1)*sin(x)+cos(x)]]
 (15)
Type: List(List(Expression(Integer)))
fricas
A:=matrix[[cos(x),-sin(x)],[sin(x),cos(x)]]
 (16)
Type: Matrix(Expression(Integer))
fricas
v:=matrix[[v11],[v12]]
 (17)
Type: Matrix(Polynomial(Integer))
fricas
C:=A*v-L(1,1)*v
 (18)
Type: Matrix(Expression(Integer))
fricas
solve(C(1,1)=0,v11)
 (19)
Type: List(Equation(Expression(Integer)))
fricas
solve(C(2,1)=0,v12)
 (20)
Type: List(Equation(Expression(Integer)))
fricas
V:=matrix[[1/sqrt(-1),1],[1,-1/sqrt(-1)]]
 (21)
Type: Matrix(AlgebraicNumber?)
fricas
Z:=matrix[[V(2,2),-V(1,2)],[-V(2,1),V(1,1)]]
 (22)
Type: Matrix(AlgebraicNumber?)
fricas
V(1,1)*V(2,2)
 (23)
Type: AlgebraicNumber?
fricas
V(1,2)*V(2,1)
 (24)
Type: AlgebraicNumber?

fricas
N:=matrix[[0],[0]]
 (25)
Type: Matrix(NonNegativeInteger?)
fricas
L:=[[sqrt(-1)*sin(x)+cos(x)],[-sqrt(-1)*sin(x)+cos(x)]]
 (26)
Type: List(List(Expression(Integer)))
fricas
A:=matrix[[cos(x),-sin(x)],[sin(x),cos(x)]]
 (27)
Type: Matrix(Expression(Integer))
fricas
v:=matrix[[v11],[v12]]
 (28)
Type: Matrix(Polynomial(Integer))
fricas
C:=A*v-L(1,1)*v
 (29)
Type: Matrix(Expression(Integer))
fricas
solve(C(1,1)=0,v11)
 (30)
Type: List(Equation(Expression(Integer)))
fricas
solve(C(2,1)=0,v12)
 (31)
Type: List(Equation(Expression(Integer)))
fricas
T:=matrix[[1/sqrt(-1),1],[1,-1/sqrt(-1)]]
 (32)
Type: Matrix(AlgebraicNumber?)
fricas
a:=sqrt(T(1,1)^2+T(2,1)^2)
 (33)
Type: AlgebraicNumber?
fricas
b=sqrt(T(1,2)^2+T(2,2)^2)
 (34)
Type: Equation(Polynomial(AlgebraicNumber?))
fricas
Z:=matrix[[V(2,2),-V(1,2)],[-V(2,1),V(1,1)]]
 (35)
Type: Matrix(AlgebraicNumber?)
fricas
V(1,1)*V(2,2)
 (36)
Type: AlgebraicNumber?
fricas
V(1,2)*V(2,1)
 (37)
Type: AlgebraicNumber?

fricas
N:=matrix[[0],[0]]
 (38)
Type: Matrix(NonNegativeInteger?)
fricas
L:=[[sqrt(-1)*sin(x)+cos(x)],[-sqrt(-1)*sin(x)+cos(x)]]
 (39)
Type: List(List(Expression(Integer)))
fricas
A:=matrix[[cos(x),-sin(x)],[sin(x),cos(x)]]
 (40)
Type: Matrix(Expression(Integer))
fricas
v:=matrix[[v11],[v12]]
 (41)
Type: Matrix(Polynomial(Integer))
fricas
C:=A*v-L(1,1)*v
 (42)
Type: Matrix(Expression(Integer))
fricas
solve(C(1,1)=0,v11)
 (43)
Type: List(Equation(Expression(Integer)))
fricas
solve(C(2,1)=0,v12)
 (44)
Type: List(Equation(Expression(Integer)))
fricas
T:=matrix[[1/sqrt(-1),1],[1,-1/sqrt(-1)]]
 (45)
Type: Matrix(AlgebraicNumber?)
fricas
sqrt(T(1,1)^2+T(2,1)^2)
 (46)
Type: AlgebraicNumber?
fricas
sqrt(T(1,2)^2+T(2,2)^2)
 (47)
Type: AlgebraicNumber?
fricas
Z:=matrix[[V(2,2),-V(1,2)],[-V(2,1),V(1,1)]]
 (48)
Type: Matrix(AlgebraicNumber?)
fricas
V(1,1)*V(2,2)
 (49)
Type: AlgebraicNumber?
fricas
V(1,2)*V(2,1)
 (50)
Type: AlgebraicNumber?

fricas
)clear all
All user variables and function definitions have been cleared.
B := %i*sqrt(a^2 + b^2 + c^2)
 (51)
Type: Expression(Complex(Integer))
fricas
A := matrix[ [B, c, -b], [-c, B, a], [b, -a, B] ]
 (52)
Type: Matrix(Expression(Complex(Integer)))
fricas
rowEchelon(A)
 (53)
Type: Matrix(Expression(Complex(Integer)))
fricas
B := -%i*sqrt(a^2 + b^2 + c^2)
 (54)
Type: Expression(Complex(Integer))
fricas
A := matrix[ [B, c, -b], [-c, B, a], [b, -a, B] ]
 (55)
Type: Matrix(Expression(Complex(Integer)))
fricas
rowEchelon(A)
 (56)
Type: Matrix(Expression(Complex(Integer)))

Write:
  \begin{axiom}
M := matrix [[1,1,1,1],[a,a,b,b],[1,1,1,1],[a,a,b,b]]
\end{axiom}


fricas
M := matrix [[1,1,1,1],[a,a,b,b],[1,1,1,1],[a,a,b,b]]
 (57)
Type: Matrix(Polynomial(Integer))