How many degree of liberty exist, actually, in a matrix 2x2 ?(adsbygoogle = window.adsbygoogle || []).push({});

Ithinkthat is three! Because the conic equation can be wrote like this:

[tex]

\begin{bmatrix}

A & B\\

C & D

\end{bmatrix}

:\begin{bmatrix}

x^2 & xy\\

yx & y^2

\end{bmatrix}

+

\begin{bmatrix}

E\\

F

\end{bmatrix}

\cdot

\begin{bmatrix}

x\\

y

\end{bmatrix}

+G=0

[/tex]

But, xy = yx, thus ... + Bxy + Cyx +... = ... + (B+C)xy + ...

So: [tex]

\begin{bmatrix}

A & (B+C)\\

0 & D

\end{bmatrix}

:\begin{bmatrix}

x^2 & xy\\

yx & y^2

\end{bmatrix}

+

\begin{bmatrix}

E\\

F

\end{bmatrix}

\cdot

\begin{bmatrix}

x\\

y

\end{bmatrix}

+G=0

[/tex]

Another example: the coefficients of the equation Ay'' + By' + Cy = 0 has three degree of liberty (A, B and C) and it can be converted in a matrix:

y' = a y + b y'

y'' = c y + d y'

So, exist more and more examples that I could give here. But, the felling that I have is the a matrix 2x2 has 3 degree of liberty, although of has four coefficients... My feeling is correct?

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# Degree of liberty of a matrix 2x2

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