 by jupiyam
Published: August 4, 2022 (2 weeks ago)
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Change of basis and projection maps

Good day,
I am somewhat confused regarding basic orthogonal projections (onto subspaces in \$mathbb{R}^n\$).
Lets assume that \$Wsubset mathbb{R}^n\$ is a subspace and \$mathbb{P_W} = mathbb{P}_W(x,y)\$ is the orthogonal projection from \$mathbb{R}^n\$ onto \$W\$.
I know that \$mathbb{P_W}\$ is also represented in the original basis as a matrix and that its column vectors form a basis for \$W\$, because \$\$mathbb{P_W} : mathbb{R}^n to mathbb{R}^n \ v mapsto P_Wv = sum_{j=1}^n a_jb_jv,\$\$
where \$a_j\$ and \$b_j\$ are the \$j\$-th column vectors of the matrices representing \$mathbb{P}_W\$ in the two basis (they both have the same size).
Now, let’s say that the new basis of \$mathbb{R}^n\$ is \$[v_1, ldots, v_n]\$ and the column vectors of the matrix of \$mathbb{P}_W\$ in the new basis are denoted \$d_1, ldots, d_n\$.
I know that the coordinates of \$d_j\$ with respect to the new basis are precisely the projections of the coordinates of \$v_j\$ onto \$W\$, i.e.:
\$\$[d_1, ldots, d_n] = [mathbb{P}_W(v_1), ldots, mathbb{P}_W(v_n)].\$\$
Now, I am confused:
When I go through my book and see that the \$d_j\$’s form a basis of \$W\$, I can’t understand

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How to get value from xml with namespace in lxml

I want to get the value from the below xml by lxml.

I have tried to access the VALUE using the below code:
root = etree.parse(mypath)
i = root.find(“{“)
i.find(“{“).text

But it throws an error as:
Value error
Tried adding namespaces to the xpath but it doesn’t