Data update

Task/Singular-value-decomposition/00-TASK.txt

@@ -1,11 +1,11 @@
-<math>A</math> is any m by n matrix, square or rectangular. Its rank is r. We will diagonalize this A, but not by <math>X^{−1}AX</math>.
+<math>A</math> is any m by n matrix, square or rectangular. Its rank is r. We will diagonalize this A, but not by <math>X^{-1} A X</math>.
 The eigenvectors in <math>X</math> have three big problems: They are usually not orthogonal, there
-are not always enough eigenvectors, and <math>Ax</math> = <math>λx</math> requires <math>A</math> to be a square matrix. The
+are not always enough eigenvectors, and <math>Ax</math> = <math>\lambda x</math> requires <math>A</math> to be a square matrix. The
 singular vectors of <math>A</math> solve all those problems in a perfect way.   
 
 [https://math.mit.edu/classes/18.095/2016IAP/lec2/SVD_Notes.pdf The Singular Value Decomposition (SVD)]   
 
-According to the web page above, for any rectangular matrix <math>A</math>, we can decomposite it as <math>A=UΣV^T</math>
+According to the web page above, for any rectangular matrix <math>A</math>, we can decomposite it as <math>A=U\Sigma V^T</math>
 
 ''' Task Description'''   
 
@@ -13,7 +13,7 @@ Firstly, input two numbers "m" and "n".
 
 Then, input a square/rectangular matrix <math>A^{m\times n}</math>.   
 
-Finally, output <math>U,Σ,V</math> with respect to <math>A</math>.
+Finally, output <math>U,~\Sigma,\ V</math> with respect to <math>A</math>.
 
 ''' Example '''   
 

Task/Singular-value-decomposition/FreeBASIC/singular-value-decomposition.basic

@@ -1,4 +1,4 @@
-#include once "g:\FreeBASIC\inc\gsl\gsl_linalg.bi"
+#include once "inc\gsl\gsl_linalg.bi"
 
 Sub MatrixPrint(r As Integer, c As Integer, m() As Double)
     For i As Integer = 0 To r - 1