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@@ -236,6 +300,38 @@ <h1><a href="../../../../index.html">All files</a> / <a href="index.html">lapack
236300/**
237301* LAPACK routine to compute the Schur factorization of a real 2-by-2 nonsymmetric matrix `A` in standard form.
238302*
303+ * Given a real 2×2 matrix:
304+ *
305+ * ```tex
306+ * \begin{bmatrix}
307+ * A & B \\
308+ * C & D
309+ * \end{bmatrix}
310+ * ```
311+ *
312+ * this routine computes an orthogonal matrix:
313+ *
314+ * ```tex
315+ * \begin{bmatrix}
316+ * \text{CS} & \text{SN} \\
317+ * -\text{SN} & \text{CS}
318+ * \end{bmatrix}
319+ * ```
320+ *
321+ * such that the matrix is reduced to Schur (quasi-triangular) form:
322+ *
323+ * ```tex
324+ * \begin{bmatrix}
325+ * \text{AA} & \text{BB} \\
326+ * \text{CC} & \text{DD}
327+ * \end{bmatrix}
328+ * ```
329+ *
330+ * where either:
331+ *
332+ * - `CC` = 0, `AA` and `DD` are the real eigenvalues of the matrix.
333+ * - `AA` = `DD` and `BB * CC` < 0, `AA + sqrt( BB * CC )` and `AA - sqrt( BB * CC )` are the complex conjugate eigenvalues.
334+ *
239335* @module @stdlib/lapack/base/dlanv2
240336*
241337* @example
@@ -295,7 +391,7 @@ <h1><a href="../../../../index.html">All files</a> / <a href="index.html">lapack
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296392 Code coverage generated by
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