Editing Main diagonal (section)

==Antidiagonal==

{{see also|Anti-diagonal matrix}}

The '''antidiagonal''' (sometimes '''counter diagonal''', '''secondary diagonal''' (*), '''trailing diagonal''', '''minor diagonal''', '''off diagonal''', or '''bad diagonal''') of an order <math>N</math> [[square matrix]] <math>B</math> is the collection of entries <math>b_{i,j}</math> such that <math>i + j = N+1</math> for all <math>1 \leq i, j \leq N</math>. That is, it runs from the top right corner to the bottom left corner.
:<math>\begin{bmatrix}
0 & 0 & \color{red}{1}\\
0 & \color{red}{1} & 0\\
\color{red}{1} & 0 & 0\end{bmatrix}</math>

(*) '''''Secondary''''' (as well as ''trailing'', ''minor'' and ''off'') diagonals very often also mean the (a.k.a. ''k''-th) diagonals '''''parallel''''' to the main or principal diagonals, ''i.e.'', <math>A_{i,\,i\pm k}</math> for some nonzero k =1, 2, 3, ... More generally and universally, the '''''off diagonal''''' elements of a matrix are all elements ''not'' on the main diagonal, ''i.e.'', with distinct indices ''i &ne; j''.