# from the theory of proveit.linear_algebra.matrices¶

see dependencies

In [1]:
import proveit
# Automation is not needed when only building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
# import the special expression
from proveit.linear_algebra.matrices import eigen_pow

In [2]:
# check that the built expression is the same as the stored expression
assert eigen_pow.expr == stored_expr
assert eigen_pow.expr._style_id == stored_expr._style_id
print("Passed sanity check: eigen_pow matches stored_expr")

Passed sanity check: eigen_pow matches stored_expr

In [3]:
# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\forall_{k \in \mathbb{N}^+}~\left[\forall_{b \in \mathbb{C}}~\left[\forall_{A, x}~\left(\left(\left(A \thinspace x\right) = \left(b \cdot x\right)\right) \Rightarrow \left(\left(A^{k} \thinspace x\right) = \left(b^{k} \cdot x\right)\right)\right)\right]\right]

In [4]:
stored_expr.style_options()

namedescriptiondefaultcurrent valuerelated methods
with_wrappingIf 'True', wrap the Expression after the parametersNoneNone/False('with_wrapping',)
condition_wrappingWrap 'before' or 'after' the condition (or None).NoneNone/False('with_wrap_after_condition', 'with_wrap_before_condition')
wrap_paramsIf 'True', wraps every two parameters AND wraps the Expression after the parametersNoneNone/False('with_params',)
justificationjustify to the 'left', 'center', or 'right' in the array cellscentercenter('with_justification',)
In [5]:
# display the expression information
stored_expr.expr_info()

core typesub-expressionsexpression
0Operationoperator: 15
operand: 2
1ExprTuple2
2Lambdaparameter: 47
body: 4
3ExprTuple47
4Conditionalvalue: 5
condition: 6
5Operationoperator: 15
operand: 9
6Operationoperator: 17
operands: 8
7ExprTuple9
8ExprTuple47, 10
9Lambdaparameter: 46
body: 12
10Literal
11ExprTuple46
12Conditionalvalue: 13
condition: 14
13Operationoperator: 15
operand: 19
14Operationoperator: 17
operands: 18
15Literal
16ExprTuple19
17Literal
18ExprTuple46, 20
19Lambdaparameters: 33
body: 21
20Literal
21Operationoperator: 22
operands: 23
22Literal
23ExprTuple24, 25
24Operationoperator: 27
operands: 26
25Operationoperator: 27
operands: 28
26ExprTuple29, 30
27Literal
28ExprTuple31, 32
29Operationoperator: 35
operands: 33
30Operationoperator: 37
operands: 34
31Operationoperator: 35
operands: 36
32Operationoperator: 37
operands: 38
33ExprTuple45, 41
34ExprTuple46, 41
35Literal
36ExprTuple39, 41
37Literal
38ExprTuple40, 41
39Operationoperator: 43
operands: 42
40Operationoperator: 43
operands: 44
41Variable
42ExprTuple45, 47
43Literal
44ExprTuple46, 47
45Variable
46Variable
47Variable