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Main diagonal
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<p>In <a href="/facts/Linear_algebra/8VaB4VWk">linear algebra</a>, the main diagonal (sometimes principal diagonal, primary diagonal, leading diagonal, major diagonal, or good diagonal) of a <a href="/facts/Matrix_(mathematics)/qa8FI4ko">matrix</a> A {\displaystyle A} is the list of entries a i , j {\displaystyle a_{i,j}} where i = j {\displaystyle i=j} . All <a href="/facts/Off-diagonal_element/39z9sIRb">off-diagonal elements</a> are <a href="/facts/Zero/Cxg56PNn">zero</a> in a <a href="/facts/Diagonal_matrix/tjIAHrE6">diagonal matrix</a>. The following four matrices have their main diagonals indicated by red ones: </p><p> [ 1 0 0 0 1 0 0 0 1 ] [ 1 0 0 0 0 1 0 0 0 0 1 0 ] [ 1 0 0 0 1 0 0 0 1 0 0 0 ] [ 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 ] {\displaystyle {\begin{bmatrix}\color {red}{1}&0&0\\0&\color {red}{1}&0\\0&0&\color {red}{1}\end{bmatrix}}\qquad {\begin{bmatrix}\color {red}{1}&0&0&0\\0&\color {red}{1}&0&0\\0&0&\color {red}{1}&0\end{bmatrix}}\qquad {\begin{bmatrix}\color {red}{1}&0&0\\0&\color {red}{1}&0\\0&0&\color {red}{1}\\0&0&0\end{bmatrix}}\qquad {\begin{bmatrix}\color {red}{1}&0&0&0\\0&\color {red}{1}&0&0\\0&0&\color {red}{1}&0\\0&0&0&\color {red}{1}\end{bmatrix}}} </p>