diff --git a/Book4_Ch20_Python_Codes/Streamlit_Bk4_Ch20_04.py b/Book4_Ch20_Python_Codes/Streamlit_Bk4_Ch20_04.py
index 11055ff..802d198 100644
--- a/Book4_Ch20_Python_Codes/Streamlit_Bk4_Ch20_04.py
+++ b/Book4_Ch20_Python_Codes/Streamlit_Bk4_Ch20_04.py
@@ -91,7 +91,7 @@ st.latex(r'''\Sigma = \begin{bmatrix}%s & %s\\%s & %s\end{bmatrix}'''
            rho_12*sigma_1*sigma_2, 
            rho_12*sigma_1*sigma_2, 
            sigma_2**2))
-
+st.latex(r'''\Sigma = V \Lambda V^{T}''')
 st.latex(bmatrix(Sigma) + '=' + 
          bmatrix(np.around(V, decimals=3)) + '@' + 
          bmatrix(np.around(D, decimals=3)) + '@' + 
diff --git a/Book4_Ch21_Python_Codes/Streamlit_Bk4_Ch21_02.py b/Book4_Ch21_Python_Codes/Streamlit_Bk4_Ch21_02.py
index 9b4c1da..188b257 100644
--- a/Book4_Ch21_Python_Codes/Streamlit_Bk4_Ch21_02.py
+++ b/Book4_Ch21_Python_Codes/Streamlit_Bk4_Ch21_02.py
@@ -60,7 +60,7 @@ D,V = np.linalg.eig(A)
 D = np.diag(D)
 
 st.latex(r'''A = \begin{bmatrix}%s & %s\\%s & %s\end{bmatrix}''' %(a, b, b, c))
-
+st.latex(r'''A = V \Lambda V^{T}''')
 st.latex(bmatrix(A) + '=' + 
          bmatrix(np.around(V, decimals=3)) + '@' + 
          bmatrix(np.around(D, decimals=3)) + '@' +