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Main diagonal

 
WordNet: main diagonal
Note: click on a word meaning below to see its connections and related words.

The noun has one meaning:

Meaning #1: the diagonal of a square matrix running from the upper left entry to the lower right entry
  Synonym: principal diagonal


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In linear algebra, the main diagonal (sometimes leading diagonal or primary diagonal) of a matrix A is the collection of cells Ai,j where i is equal to j.

The main diagonal of a square matrix is the diagonal which runs from the top left corner to the bottom right corner. For example, the following matrix has 1s down its main diagonal:

\begin{bmatrix}
1 & 0 & 0\\
0 & 1 & 0\\
0 & 0 & 1\end{bmatrix}.

A square matrix like the above in which the entries outside the main diagonal are all zero is called a diagonal matrix. The sum of the entries on the main diagonal of a matrix is known as the trace of that matrix.

The main diagonal of a rectangular matrix is the diagonal which runs from the top left corner and steps down and right, until the right edge is reached.

\begin{bmatrix}
1 & 0 & 0 & 0 \\
0 & 1 & 0 & 0 \\
0 & 0 & 1 & 0 \end{bmatrix}


\begin{bmatrix}
1 & 0 & 0\\
0 & 1 & 0\\
0 & 0 & 1\\
0 & 0 & 0\end{bmatrix}

The other diagonal is called antidiagonal, counterdiagonal, secondary diagonal, or minor diagonal.

References


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Some good "Main diagonal" pages on the web:


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Wikipedia. This article is licensed under the Creative Commons Attribution/Share-Alike License. It uses material from the Wikipedia article "Main diagonal" Read more