Sep 19, 2021 · Upper Triangular Matrix. A triangular matrix of the form. (1) Written explicitly, (2) A matrix can be tested to determine if it is upper triangular in the Wolfram Language using UpperTriangularMatrixQ [ m ]. A strictly upper triangular matrix is an upper triangular matrix having 0s along the diagonal as well, i.e., for .
Hence, by induction, there is a unique lower-triangular matrix $\Lambda_{11}$ with positive diagonal elements satisfying the first equation. We can then obtain $\bfbeta_{12}$ from the second equation by forward substitution.