projextion matrix symbolic polar

src/linear_algebra_transform.jl

@@ -1,15 +1,22 @@
 using Symbolics
 include("./linear_algebra_basic.jl")
 
+@variables u v
 """
     function projection_matrix_symbolic() -> Matrix
-Create matrix for projection on [u, v] using E₁ = [1,0] and E₂ =[0,1]
+Create symbolic matrix for projection on [u, v] using E₁ = [1,0] and E₂ =[0,1] to get first and second row
 """
 function projection_matrix_symbolic()
-    [orthproj([u, v], [1, 0])[1] orthproj([u, v], [1, 0])[2]; orthproj([u, v], [0, 1])[1] orthproj([u, v], [0, 1])[2]]
+    [orthproj([u, v], [1, 0])[1] orthproj([u, v], [0, 1])[1]; orthproj([u, v], [1, 0])[2] orthproj([u, v], [0, 1])[2]]
 end
 
+function projection_matrix_symbolic_polar()
+    simplify.(substitute.(projection_matrix_symbolic(),(Dict(u => cos(θ), v => sin(θ)),)))
+end
+"""
+    function projection_matrix(x::Vector) -> Matrix
+value of Matrix with an actual x  
+"""
 function projection_matrix(x::Vector)
     Symbolics.value.(substitute.(projection_matrix_symbolic(), (Dict(u =>x[1], v=> x[2]), )))
 end
-