Re: [Boost-users] [uBLAS] Matrix inversion

Subject: Re: [Boost-users] [uBLAS] Matrix inversion
From: Bo Jensen (jensen.bo_at_[hidden])
Date: 2011-03-02 15:19:04

On Wed, Mar 2, 2011 at 8:07 PM, Matwey V. Kornilov
<matwey.kornilov_at_[hidden]> wrote:
>
> A triangular matrix has zero elements below the diagonal (upper triangular)
> or above the diagonal (lower triangular). This way a nonsingular triangular
> matrix can be inverted in straightforward manner. LU decomposition allows to
> produce two triangular matrices which product is your source matrix. A
> matrix inversion can be implemented by means of these succeeding operations.
>

Even the matrix is triangular, you still don't invert it, you use
forward and backward substitution to solve the linear system. I am
sorry to be a pain, but I think this thread needs to be concise about
the use of inverse.

> Ryan wrote:
>
>> Matwey V. Kornilov wrote:
>>> `solve' does matrix inversion for triangular matrices. LU decomposition
>>> is also present in lu.hpp
>>>
>>>
>> What is the difference between a triangular matrix and the plain matrix?
>>
>> Ryan
>
>
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