- #1
twoflower
- 368
- 0
Hi all,
I don't understand one thing about linearity of determinants. In the book I have:
[tex]
\det \left( \begin{array}{ccc} . & . & . \\ . & . & . \\ \mbox{} \\ . & . & . \\ . & . & . \\ . & . & . \\ \mbox{[j]} \end{array} \right) = \det \left( \begin{array}{ccc} . & . & . \\ . & . & . \\ \mbox{} \\ . & . & . \\ . & . & . \\ . & . & . \\ \mbox{[j+i]} \end{array} \right)
[/tex]
And the explanation is:
[tex]
\det \left( \begin{array}{ccc} . & . & . \\ . & . & . \\ \mbox{} \\ . & . & . \\ . & . & . \\ . & . & . \\ \mbox{[j+i]} \end{array} \right) = \det \left( \begin{array}{ccc} . & . & . \\ . & . & . \\ \mbox{} \\ . & . & . \\ . & . & . \\ . & . & . \\ \mbox{[j]} \end{array} \right) + \det \left( \begin{array}{ccc} . & . & . \\ . & . & . \\ \mbox{} \\ . & . & . \\ . & . & . \\ . & . & . \\ \mbox{} \end{array} \right)
[/tex]
But I can't see how these two matrixes (I mean now left and right side of the bottom equation) can be identical, because when I sum the two matrixes on the right, I won't get the matrix on the left...
Thank you for the explanation.
I don't understand one thing about linearity of determinants. In the book I have:
[tex]
\det \left( \begin{array}{ccc} . & . & . \\ . & . & . \\ \mbox{} \\ . & . & . \\ . & . & . \\ . & . & . \\ \mbox{[j]} \end{array} \right) = \det \left( \begin{array}{ccc} . & . & . \\ . & . & . \\ \mbox{} \\ . & . & . \\ . & . & . \\ . & . & . \\ \mbox{[j+i]} \end{array} \right)
[/tex]
And the explanation is:
[tex]
\det \left( \begin{array}{ccc} . & . & . \\ . & . & . \\ \mbox{} \\ . & . & . \\ . & . & . \\ . & . & . \\ \mbox{[j+i]} \end{array} \right) = \det \left( \begin{array}{ccc} . & . & . \\ . & . & . \\ \mbox{} \\ . & . & . \\ . & . & . \\ . & . & . \\ \mbox{[j]} \end{array} \right) + \det \left( \begin{array}{ccc} . & . & . \\ . & . & . \\ \mbox{} \\ . & . & . \\ . & . & . \\ . & . & . \\ \mbox{} \end{array} \right)
[/tex]
But I can't see how these two matrixes (I mean now left and right side of the bottom equation) can be identical, because when I sum the two matrixes on the right, I won't get the matrix on the left...
Thank you for the explanation.