docs: add an intro in readme with math tags

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---

Author: aayush0325

lib/node_modules/@stdlib/lapack/base/dlaqr1/README.md

@@ -22,6 +22,67 @@ limitations under the License.
 
 > Given a 2-by-2 or a 3-by-3 matrix `H`, this LAPACK routine sets `V` to a scalar multiple of the first column of `K` where `K = (H - (sr1 + i*si1)*I)*(H - (sr2 + i*si2)*I)`.
 
+<section class="intro">
+
+The `dlaqr1` routine computes a scalar multiple of the first column of a matrix `K` defined by the product of two shifted matrices. Given a matrix `H` and two complex shifts (which may be conjugates), the routine constructs:
+
+<!-- <equation class="equation" label="eq:matrix_k" align="center" raw="K = (H - (sr_1 + i \cdot si_1) \cdot I) \cdot (H - (sr_2 + i \cdot si_2) \cdot I)" alt="Definition of matrix K."> -->
+
+```math
+K = (H - (sr_1 + i \cdot si_1) \cdot I) \cdot (H - (sr_2 + i \cdot si_2) \cdot I)
+```
+
+<!-- </equation> -->
+
+where:
+
+-   `H` is an N-by-N matrix (N = 2 or 3)
+-   `sr1, si1` represent the real and imaginary parts of the first shift
+-   `sr2, si2` represent the real and imaginary parts of the second shift
+-   `I` is the identity matrix
+
+The routine extracts the first column of `K` and stores it as a scalar multiple in the output vector `V`. For a 2-by-2 matrix `H`:
+
+<!-- <equation class="equation" label="eq:matrix_h_2x2" align="center" raw="H = \left[\begin{array}{cc}h_{11} & h_{12} \\h_{21} & h_{22}\end{array}\right]" alt="2-by-2 matrix H."> -->
+
+```math
+H = \left[
+\begin{array}{cc}
+h_{11} & h_{12} \\
+h_{21} & h_{22}
+\end{array}
+\right]
+```
+
+<!-- </equation> -->
+
+For a 3-by-3 matrix `H`:
+
+<!-- <equation class="equation" label="eq:matrix_h_3x3" align="center" raw="H = \left[\begin{array}{ccc}h_{11} & h_{12} & h_{13} \\h_{21} & h_{22} & h_{23} \\h_{31} & h_{32} & h_{33}\end{array}\right]" alt="3-by-3 matrix H."> -->
+
+```math
+H = \left[
+\begin{array}{ccc}
+h_{11} & h_{12} & h_{13} \\
+h_{21} & h_{22} & h_{23} \\
+h_{31} & h_{32} & h_{33}
+\end{array}
+\right]
+```
+
+<!-- </equation> -->
+
+The shifts are typically complex conjugate pairs, meaning either:
+
+1.  `sr1 = sr2` and `si1 = -si2` (conjugate complex shifts), or
+2.  `si1 = si2 = 0` (real shifts)
+
+This routine is particularly useful in the QR algorithm for starting double implicit shift bulges, where the computed vector `V` defines the Householder reflector for the implicit shift step.
+
+</section>
+
+<!-- /.intro -->
+
 <section class="usage">
 
 ## Usage
@@ -248,7 +309,7 @@ TODO
 
 [lapack]: https://www.netlib.org/lapack/explore-html/
 
-[lapack-dlaqr1]: https://www.netlib.org/lapack/explore-html/d1/d72/dlaqr1_8f.html
+[lapack-dlaqr1]: https://netlib.org/lapack/explore-html/d3/d57/group__laqr1_ga72fe4989b96418ec66d6ee18b4ac23e8.html
 
 [mdn-float64array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Float64Array