minor update

index.html

@@ -137,7 +137,7 @@ <h2>The Spectrum of a Tensor Field</h2>
 \end{align}
 \]</span></p><p>There is no need to know these values when getting the product tables <span class="math inline">\(X_{i}X_{j}\)</span>.</p>
 
-<p><a href="https://aapt.scitation.org/doi/10.1119/1.1976018">Shankland (1970)</a> applies <a href="https://en.wikipedia.org/wiki/Faddeev%E2%80%93LeVerrier_algorithm">the Faddeev - LeVerrier algorithm</a>, or rather its advanced variant extended to tackle multiple eigenvalues, see e.g. <a href="https://core.ac.uk/download/pdf/81192811.pdf">Helmberg and Wagner (1993)</a>. Note also that here we do not have eigenvectors in a traditional sense, they are weighted sums of the basis <span class="math inline">\(X_{i}\)</span>, not some matrix columns.</p>
+<p><a href="https://aapt.scitation.org/doi/10.1119/1.1976018">Shankland (1970)</a> applies <a href="https://en.wikipedia.org/wiki/Faddeev%E2%80%93LeVerrier_algorithm">the Faddeev - LeVerrier algorithm</a>, or rather its advanced variant extended to tackle multiple eigenvalues, see e.g. <a href="https://core.ac.uk/download/pdf/81192811.pdf">Helmberg and Wagner (1993)</a>. Here there are no eigenvectors in a traditional sense, they are weighted sums of the basis <span class="math inline">\(X_{i}\)</span>, not some matrix columns.</p>
 
 <p><a href="https://spiral.imperial.ac.uk/bitstream/10044/1/13413/2/Barnes-KJ-1963-PhD-Thesis.pdf">K.J. Barnes (1963)</a> seeks the spectrum differently, with the matrix projection operators.</p>
 
@@ -175,7 +175,7 @@ <h2>Why Shankland?</h2>
 
 <p>To sum up, we are given a field with tensor/spinor indices and their permutation symmetries. The author shows how to build a Lorentz-invariant operator which may serve as a quadratic form for the field. The invented (discovered?!) machinery allows to control a spin content of the field, defined as the eigenvalue multiplicities of the general element of the field&rsquo;s algebra. One test of this formalism confirms that removing spin 0 from a vector field leads to &ldquo;apesanteur&rdquo; <span class="math inline">\(A\)</span> aka vector potential.</p>
 
-<p>Considering a massive literature around group theory, irreducible representations, angular momentum, higher spin field theories, spin projection operators, tensors, spinors, Weyl, Wigner, Weinberg&hellip; <strong>Shankland&rsquo;s system is the only one I can really follow.</strong></p>
+<p>Considering a massive literature around group theory, irreducible representations, angular momentum, higher spin field theories, spin projection operators, tensors, spinors, Weyl, Wigner, Weinberg&hellip; <strong>Shankland&rsquo;s system is the only one I can really follow!</strong></p>
 
 <div class="imgcontainer">
 <a style="font-size: 1.5rem;" href="https://youtu.be/Y183gJQ9yCY?t=20">Sign the contract big boy...</a>

index.md

@@ -135,7 +135,7 @@ $$
 
 There is no need to know these values when getting the product tables $X_{i}X_{j}$. 
 
-[Shankland (1970)](https://aapt.scitation.org/doi/10.1119/1.1976018) applies [the Faddeev - LeVerrier algorithm](https://en.wikipedia.org/wiki/Faddeev%E2%80%93LeVerrier_algorithm), or rather its advanced variant extended to tackle multiple eigenvalues, see e.g. [Helmberg and Wagner (1993)](https://core.ac.uk/download/pdf/81192811.pdf). Note also that here we do not have eigenvectors in a traditional sense, they are weighted sums of the basis $X_{i}$, not some matrix columns.
+[Shankland (1970)](https://aapt.scitation.org/doi/10.1119/1.1976018) applies [the Faddeev - LeVerrier algorithm](https://en.wikipedia.org/wiki/Faddeev%E2%80%93LeVerrier_algorithm), or rather its advanced variant extended to tackle multiple eigenvalues, see e.g. [Helmberg and Wagner (1993)](https://core.ac.uk/download/pdf/81192811.pdf). Here there are no eigenvectors in a traditional sense, they are weighted sums of the basis $X_{i}$, not some matrix columns.
 
 [K.J. Barnes (1963)](https://spiral.imperial.ac.uk/bitstream/10044/1/13413/2/Barnes-KJ-1963-PhD-Thesis.pdf) seeks the spectrum differently, with the matrix projection operators.
 
@@ -171,7 +171,7 @@ It is tough to read this literature, and the results may not always justify the
 
 To sum up, we are given a field with tensor/spinor indices and their permutation symmetries. The author shows how to build a Lorentz-invariant operator which may serve as a quadratic form for the field. The invented (discovered?!) machinery allows to control a spin content of the field, defined as the eigenvalue multiplicities of the general element of the field's algebra. One test of this formalism confirms that removing spin 0 from a vector field leads to "apesanteur" $A$ aka vector potential.
 
-Considering a massive literature around group theory, irreducible representations, angular momentum, higher spin field theories, spin projection operators, tensors, spinors, Weyl, Wigner, Weinberg... **Shankland's system is the only one I can really follow.**
+Considering a massive literature around group theory, irreducible representations, angular momentum, higher spin field theories, spin projection operators, tensors, spinors, Weyl, Wigner, Weinberg... **Shankland's system is the only one I can really follow!**
 
 <div class="imgcontainer">
 <a style="font-size: 1.5rem;" href="https://youtu.be/Y183gJQ9yCY?t=20">Sign the contract big boy...</a>