polar projection

src/linear_algebra_transform.jl

@@ -1,22 +1,33 @@
 using Symbolics
 include("./linear_algebra_basic.jl")
 
-@variables u v
 """
     function projection_matrix_symbolic() -> Matrix
 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()
+    @variables u v
     [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() -> Matrix
+Create symbolic matrix for projection on [cos θ, sin θ] 
+"""
 function projection_matrix_symbolic_polar()
+    @variables u v θ
     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  
+value of Matrix with an actual vector x  
 """
 function projection_matrix(x::Vector)
     Symbolics.value.(substitute.(projection_matrix_symbolic(), (Dict(u =>x[1], v=> x[2]), )))
 end
+"""
+    function projection_matrix_polar(θ::Number) -> Matrix
+value of Matrix with an actual value for the angle of the vector
+"""
+function projection_matrix_polar(n::Number)
+    Symbolics.value.(substitute.(projection_matrix_symbolic_polar(), θ => deg2rad(n),))
+end