Linear algebra (determinants, eigenvalues, elimination) about sympy

[certik]

**Owner:** ---  

Original comment: http://code.google.com/p/sympy/issues/detail?id=15#c1

Original author: https://code.google.com/u/104039945248245758823/

[certik]

Working on this. As an application, I chose calculations of matrix elements in the
quantum field theory.

**Status:** Started  
**Owner:** ondrej.certik  

Original comment: http://code.google.com/p/sympy/issues/detail?id=15#c2

Original author: https://code.google.com/u/104039945248245758823/

[certik]

The symbolic matrices are quite a special kind of objects, because they are not
immutable, contrary to all other sympy classes. We want them to be used as:

a = Matrix( [ [1,0], [0,1] ])
a[0,1] = x**2

So I think Matrix shouldn't be a subclass of Basic. If the user wants to calculate
with symbols of matrices, he can use the NCSymbol class. And if he wants to
substitute the actual matrix for the symbol, he can just some method of Matrix, or
subs(). 

The thing is, I think there is no need of storing matrices in an expression. It seems
to me, it is sufficient to always convert the whole expression with matrices to a
single matrix, which can be achieved by overloading *,+, etc for the Matrix class.

**Labels:** Milestone-Release0.3  

Original comment: http://code.google.com/p/sympy/issues/detail?id=15#c3

Original author: https://code.google.com/u/104039945248245758823/

[certik]

The basic matrices work. 

The linear algebra (determinants, Gaussian elimination, eigenvalues) still needs to
be implemented though, but I am leaving this for later, when we need this
functionality in some other algorithm.

**Status:** Accepted  
**Owner:** ---  
**Labels:** -Milestone-Release0.3  

Original comment: http://code.google.com/p/sympy/issues/detail?id=15#c4

Original author: https://code.google.com/u/104039945248245758823/

[certik]

**Summary:** Linear algebra (determinants, eigenvalues, elimination)  

Original comment: http://code.google.com/p/sympy/issues/detail?id=15#c5

Original author: https://code.google.com/u/104039945248245758823/

[certik]

BTW, for creating a 'pure symbolic' matrix, this syntax would be nice
(idea from maple):

> > > A = Matrix(2,2, symbol='x')
> > > A
> > >     [ x_1_1   x_1_2 ]
> > >     [ x_2_1   x_2_2 ]

It's only syntactic sugar. The above would be equivalent to:

> > > A = Matrix([[0,1],[1,0]])
> > > for i in range(2):
> > > ...    for j in range(2):
> > > ...        A[i, j] = Symbol('x_%s_%s' % (i, j))

But it comes handy when you create matrices that mostly have symbols
inside. I
just remembered that when I used maple, this was a time-saving way of
creating matrices that mostly store symbolic unknown values.

It comes handy when you want to calculate with the
matrix elements symbolically, but you don't know anything more about
them. Right, I agree, I'll put that into the issues.

Original comment: http://code.google.com/p/sympy/issues/detail?id=15#c6

Original author: https://code.google.com/u/104039945248245758823/

[certik]

Implemented.

**Status:** Fixed  

Original comment: http://code.google.com/p/sympy/issues/detail?id=15#c7

Original author: https://code.google.com/u/104039945248245758823/