docs: add tex equations

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Author: aayush0325

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

@@ -22,6 +22,56 @@ limitations under the License.
 
 > LAPACK routine to generate a real elementary reflector `H` of order `N` such that applying `H` to a vector `[alpha; X]` zeros out `X`.
 
+<section class="intro">
+
+The `dlarfg` routine generates a **real elementary reflector** (also known as a Householder reflector) of order `N`, which can be used to zero out selected components of a vector. Specifically, it constructs a reflector matrix `H` such that:
+
+<!-- <equation class="equation" label="eq:lu_decomposition" align="center" raw="H \cdot \begin{bmatrix}\alpha \\ x \end{bmatrix} = \begin{bmatrix} \beta \\ 0 \end{bmatrix}, \quad \text{and} \quad H^T H = I" alt="Transformation of vector [α; x] into [β; 0] using orthogonal reflector H, and condition that H is orthogonal (HᵀH = I)."> -->
+
+
+```math
+H \cdot \begin{bmatrix}\alpha \\ x \end{bmatrix} = \begin{bmatrix} \beta \\ 0 \end{bmatrix}, \quad \text{and} \quad H^T H = I
+```
+
+<!-- </equation> -->
+
+
+Here:
+
+-   `α` is a scalar.
+-   `X` is a real vector of length `N-1`.
+-   `β` is a scalar value.
+-   `H` is an orthogonal matrix known as a Householder reflector.
+
+The reflector `H` is constructed in the form:
+
+<!-- <equation class="equation" label="eq:matrix_a" align="center" raw="H = I - \tau \begin{bmatrix}1 \\ v \end{bmatrix} \begin{bmatrix}1 & v^T \end{bmatrix}" alt="Definition of Householder reflector H as identity minus tau times the outer product of the vector [1; v] with its transpose."> -->
+
+```math
+H = I - \tau \begin{bmatrix}1 \\ v \end{bmatrix} \begin{bmatrix}1 & v^T \end{bmatrix}
+```
+
+<!-- </equation> -->
+
+Where:
+
+-   `τ` (`tau`) is a real scalar.
+-   `V` is a real vector of length `N-1` that defines the Householder vector.
+-   The vector `[1; V]` is the Householder direction.
+
+The values of `τ` and `V` are chosen so that applying `H` to the vector `[α; x]` results in a new vector `[β; 0]`, i.e., only the first component remains nonzero. The reflector matrix `H` is **symmetric and orthogonal**, satisfying `H^T = H` and `H^T H = I`.
+
+### Special Cases
+
+-   If all elements of `x` are zero, then `τ = 0` and `H = I`, the identity matrix.
+-   Otherwise, `τ` satisfies `1 ≤ τ ≤ 2`, ensuring numerical stability in transformations.
+
+This elementary reflector is commonly used in algorithms for QR factorization and other orthogonal transformations.
+
+</section>
+
+<!-- /.intro -->
+
 <section class="usage">
 
 ## Usage