Main diagonal: Difference between revisions

Latest revision as of 15:34, 1 May 2014

Definition

The main diagonal or principal diagonal of a square matrix is defined as the set of positions (and corresponding entries) in the matrix where the row and column index are equal. Explicitly, suppose $n$ is a natural number and $A=(a_{ij})_{1\leq i\leq n,1\leq j\leq n}$ is a $n\times n$ square matrix. The main diagonal of $A$ is the collection of entries:

$\{a_{ii}:1\leq i\leq n\}$

In cases where there is no ambiguity, the main diagonal is simply referred to as the diagonal.

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-#redirect [[Diagonal]]
+==Definition==
+The '''main diagonal''' or '''principal diagonal''' of a [[square matrix]] is defined as the set of positions (and corresponding entries) in the matrix where the row and column index are equal. Explicitly, suppose <math>n</math> is a [[natural number]] and <math>A = (a_{ij})_{1 \le i \le n, 1 \le j \le n}</math> is a <math>n \times n</math> square matrix. The main diagonal of <math>A</math> is the collection of entries:
+<math>\{ a_{ii} : 1 \le i \le n \}</math>
+In cases where there is no ambiguity, the main diagonal is simply referred to as the '''diagonal'''.