: Mathematics: diagonal matrix

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diagonal matrix

In linear algebra, a diagonal matrix is a matrix in which the entries outside the main diagonal are all zero; the term usually refers to square matrices. Elements of the main diagonal can either be zero or nonzero. An example of a 2×2 diagonal matrix is ${\\displaystyle \\left[{\egin{smallmatrix}3&0\\\\0&2\\end{smallmatrix}}\ ight]}$ , while an example of a 3×3 diagonal matrix is ${\\displaystyle \\left[{\egin{smallmatrix}6&0&0\\\\0&5&0\\\\0&0&4\\end{smallmatrix}}\ ight]}$ . An identity matrix of any size, or any multiple of it is a diagonal matrix called scalar matrix, for example, ${\\displaystyle \\left[{\egin{smallmatrix}0.5&0\\\\0&0.5\\end{smallmatrix}}\ ight]}$ . In geometry, a diagonal matrix may be used as a scaling matrix, since matrix multiplication with it results in changing scale (size) and possibly also shape; only a scalar matrix results in uniform change in scale.
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Diagonal_matrix)