#Type/Definition #Topic/Linear_Algebra #coldwar

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Regular Matrix

Let A∈Rn×n be a "given" square matrix. We say A is regular if it reduces to an 8.9 Upper-Triangular Matrix U with all non-zero pivots in the diagonal elements using ONLY multiplication by 9.8 Shear Matrix.

  • A regular matrix is pretty much the easiest type of matrix to reduce.
  • The process of reducing regular matrices is known as regular Gaussian Elimination.

Remark. Note that regular matrices are a special subclass of matrices. In general, more sophisticated reduction algorithms will be necessary to deal with with non-regular and non-square matrices.
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