A Clear Introduction to Diagonal Matrices
A diagonal matrix is a square matrix in which every entry away from the main (leading) diagonal is zero. The leading diagonal runs from the top-left corner of the matrix to the bottom-right corner, and these diagonal entries are the only positions that may contain non-zero values. All off-diagonal entries must be zero. The diagonal entries themselves can be any real numbers, including zero. This strict structure is what makes diagonal matrices especially simple to analyse and compute with in linear algebra. Examples of Diagonal Matrices The general 2×2 diagonal matrix has the form: (a 0) (0 b) The general 3×3 diagonal matrix has the form: (a 0 0) (0 b 0) (0 0 c) In both cases, the values on the leading diagonal (a, b, c, …) are the only entries that may be non-zero. Every position above or below this diagonal is fixed at 0. The General n×n Diagonal Matrix For an n×n dia...