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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 $W\subset \mathbb{R}^n$ 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