Concept

# Diagonal matrix

Summary
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 \left[\begin{smallmatrix} 3 & 0 \ 0 & 2 \end{smallmatrix}\right], while an example of a 3×3 diagonal matrix is \left[\begin{smallmatrix} 6 & 0 & 0 \ 0 & 0 & 0 \ 0 & 0 & 0 \end{smallmatrix}\right]. An identity matrix of any size, or any multiple of it (a scalar matrix), is a diagonal matrix. A diagonal matrix is sometimes called a scaling matrix, since matrix multiplication with it results in changing scale (size). Its determinant is the product of its diagonal values. Definition As stated above, a diagonal matrix is a matrix in which all off-diagonal entries are zero. That is, the matrix D = (di,j) with n columns and n rows is diagonal if \forall i,j \in {1, 2, \ldots, n}
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