: Mathématiques: main diagonal

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main diagonal

In linear algebra, the main diagonal (sometimes principal diagonal, primary diagonal, leading diagonal, major diagonal, or good diagonal) of a matrix ${\\displaystyle A}$ is the list of entries ${\\displaystyle a_{i,j}}$ where ${\\displaystyle i=j}$ . All off-diagonal elements are zero in a diagonal matrix. The following four matrices have their main diagonals indicated by red ones: ${\\displaystyle {\egin{bmatrix}\\color {red}{1}&0&0\\\\0&\\color {red}{1}&0\\\\0&0&\\color {red}{1}\\end{bmatrix}}\\qquad {\egin{bmatrix}\\color {red}{1}&0&0&0\\\\0&\\color {red}{1}&0&0\\\\0&0&\\color {red}{1}&0\\end{bmatrix}}\\qquad {\egin{bmatrix}\\color {red}{1}&0&0\\\\0&\\color {red}{1}&0\\\\0&0&\\color {red}{1}\\\\0&0&0\\end{bmatrix}}\\qquad {\egin{bmatrix}\\color {red}{1}&0&0&0\\\\0&\\color {red}{1}&0&0\\\\0&0&\\color {red}{1}&0\\\\0&0&0&\\color {red}{1}\\end{bmatrix}}\\qquad }$
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Main_diagonal)

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