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{[/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.[/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.