- #1
Bruno Tolentino
- 97
- 0
I have a doubt...
Look this matrix equation:
[tex]\begin{bmatrix}
A\\
B
\end{bmatrix} = \begin{bmatrix}
+\frac{1}{\sqrt{2}} & +\frac{1}{\sqrt{2}}\\
+\frac{1}{\sqrt{2}} & -\frac{1}{\sqrt{2}}
\end{bmatrix} \begin{bmatrix}
X\\
Y
\end{bmatrix}[/tex]
[tex]\begin{bmatrix}
X\\
Y
\end{bmatrix} = \begin{bmatrix}
+\frac{1}{\sqrt{2}} & +\frac{1}{\sqrt{2}}\\
+\frac{1}{\sqrt{2}} & -\frac{1}{\sqrt{2}}
\end{bmatrix} \begin{bmatrix}
A\\
B
\end{bmatrix}[/tex]
By analogy, should exist a matrix 3x3 such that:
[tex]\begin{bmatrix}
A\\
B\\
C\\
\end{bmatrix} = \begin{bmatrix}
? & ? & ?\\
? & ? & ?\\
? & ? & ?\\
\end{bmatrix} \begin{bmatrix}
X\\
Y\\
Z\\
\end{bmatrix}[/tex]
[tex]\begin{bmatrix}
X\\
Y\\
Z\\
\end{bmatrix} = \begin{bmatrix}
? & ? & ?\\
? & ? & ?\\
? & ? & ?\\
\end{bmatrix} \begin{bmatrix}
A\\
B\\
C\\
\end{bmatrix}[/tex]
So, what values need be replaced in ? for the matrix equation above be right?
I think that my doubt is related with these wikipages:
https://en.wikipedia.org/wiki/Quadratic_formula#By_Lagrange_resolvents
https://en.wikipedia.org/wiki/Cubic_function#Lagrange.27s_method
https://en.wikipedia.org/wiki/Quartic_function#Solving_by_Lagrange_resolvent
EDIT: The inverse of the 3x3 matrix need be equal to itself.
Look this matrix equation:
[tex]\begin{bmatrix}
A\\
B
\end{bmatrix} = \begin{bmatrix}
+\frac{1}{\sqrt{2}} & +\frac{1}{\sqrt{2}}\\
+\frac{1}{\sqrt{2}} & -\frac{1}{\sqrt{2}}
\end{bmatrix} \begin{bmatrix}
X\\
Y
\end{bmatrix}[/tex]
[tex]\begin{bmatrix}
X\\
Y
\end{bmatrix} = \begin{bmatrix}
+\frac{1}{\sqrt{2}} & +\frac{1}{\sqrt{2}}\\
+\frac{1}{\sqrt{2}} & -\frac{1}{\sqrt{2}}
\end{bmatrix} \begin{bmatrix}
A\\
B
\end{bmatrix}[/tex]
By analogy, should exist a matrix 3x3 such that:
[tex]\begin{bmatrix}
A\\
B\\
C\\
\end{bmatrix} = \begin{bmatrix}
? & ? & ?\\
? & ? & ?\\
? & ? & ?\\
\end{bmatrix} \begin{bmatrix}
X\\
Y\\
Z\\
\end{bmatrix}[/tex]
[tex]\begin{bmatrix}
X\\
Y\\
Z\\
\end{bmatrix} = \begin{bmatrix}
? & ? & ?\\
? & ? & ?\\
? & ? & ?\\
\end{bmatrix} \begin{bmatrix}
A\\
B\\
C\\
\end{bmatrix}[/tex]
So, what values need be replaced in ? for the matrix equation above be right?
I think that my doubt is related with these wikipages:
https://en.wikipedia.org/wiki/Quadratic_formula#By_Lagrange_resolvents
https://en.wikipedia.org/wiki/Cubic_function#Lagrange.27s_method
https://en.wikipedia.org/wiki/Quartic_function#Solving_by_Lagrange_resolvent
EDIT: The inverse of the 3x3 matrix need be equal to itself.