update notations

content/CSE5313/CSE5313_L14.md

@@ -230,7 +230,7 @@ Step 1: Arrange the $B=\binom{k+1}{2}+k(d-k)$ symbols in a matrix $M$ follows:
 $$
 M=\begin{pmatrix}
 S & T\\
-T^T & 0
+T^\top & 0
 \end{pmatrix}\in \mathbb{F}_q^{d\times d}
 $$
 
@@ -267,15 +267,15 @@ Repair from (any) nodes $H = \{h_1, \ldots, h_d\}$.
 
 Newcomer contacts each $h_j$: “My name is $i$, and I’m lost.”
 
-Node $h_j$ sends $c_{h_j}M c_i^T$ (inner product).
+Node $h_j$ sends $c_{h_j}M c_i^\top$ (inner product).
 
-Newcomer assembles $C_H Mc_i^T$.
+Newcomer assembles $C_H Mc_i^\top$.
 
 $CH$ invertible by construction!
 
-- Recover $Mc_i^T$.
+- Recover $Mc_i^\top$.
 
-- Recover $c_i^TM$ ($M$ is symmetric)
+- Recover $c_i^\topM$ ($M$ is symmetric)
 
 #### Reconstruction on Product-Matrix MBR codes
 
@@ -292,9 +292,9 @@ DC assembles $C_D M$.
 
 $\Psi_D$ invertible by construction.
 
-- DC computes $\Psi_D^{-1}C_DM = (S+\Psi_D^{-1}\Delta_D^T, T)$
+- DC computes $\Psi_D^{-1}C_DM = (S+\Psi_D^{-1}\Delta_D^\top, T)$
 - DC obtains $T$.
-- Subtracts $\Psi_D^{-1}\Delta_D T^T$ from $S+\Psi_D^{-1}\Delta_D T^T$ to obtain $S$.
+- Subtracts $\Psi_D^{-1}\Delta_D T^\top$ from $S+\Psi_D^{-1}\Delta_D T^\top$ to obtain $S$.
 
 <details>
 <summary>Fill an example here please.</summary>