Hi all,(adsbygoogle = window.adsbygoogle || []).push({});

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.

**Physics Forums - The Fusion of Science and Community**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Linearity of determinant

Loading...

Similar Threads - Linearity determinant | Date |
---|---|

B Why the hate on determinants? | Jun 9, 2017 |

I Using determinant to find constraints on equation | Jan 15, 2017 |

Determine if all vectors of form (a,0,0) are subspace of R3 | Jan 21, 2015 |

Linear Algebra -finding determinant of a matrix | Oct 7, 2014 |

Wronskian vs. Determinant in Determining Linear Independence? | Jun 1, 2014 |

**Physics Forums - The Fusion of Science and Community**