xx:= matrix([[a11, a12], [a21, a22]])
+a11 a12+
| |
+a21 a22+
Type: Matrix Polynomial Integer
yy:= matrix([[y1], [y2]])
+y1+
| |
+y2+
Type: Matrix Polynomial Integer
determinant xx
a11 a22 - a12 a21
Type: Polynomial Integer
zz:= inverse(xx)*yy
+- a12 y2 + a22 y1+
|-----------------|
|a11 a22 - a12 a21|
| |
| a11 y2 - a21 y1 |
|-----------------|
+a11 a22 - a12 a21+
Type: Matrix Fraction Polynomial Integer
inverse(xx)**2
[
2
a22 + a12 a21
[--------------------------------------,
2 2 2 2
a11 a22 - 2a11 a12 a21 a22 + a12 a21
- a12 a22 - a11 a12
2 2 2 2
a11 a22 - 2a11 a12 a21 a22 + a12 a21
,
- a21 a22 - a11 a21
[--------------------------------------,
2 2 2 2
a11 a22 - 2a11 a12 a21 a22 + a12 a21
2
a12 a21 + a11
2 2 2 2
a11 a22 - 2a11 a12 a21 a22 + a12 a21
]
Type: Matrix Fraction Polynomial Integer
v := matrix([[2, -1, 1], [0, 1, 1], [-1, 1, 1]])
+ 2 - 1 1+
| |
| 0 1 1|
| |
+- 1 1 1+
Type: Matrix Integer
eigenvectors v
+0+ +1+
| | | |
[[eigval= 2,eigmult= 1,eigvec= [|1|]],[eigval= 1,eigmult= 2,eigvec= [|1|]]]
| | | |
+1+ +0+
Type: List Union(Record(algrel: Fraction Polynomial Integer,algmult: Integer,algvec: List Matrix Fraction Polynomial Integer),Record(eigval: Fraction Polynomial Integer,eigmult: Integer,eigvec: List Matrix Fraction Polynomial Integer))