How to have a label for a LaTeX table that can be referenced in HTML document

[friendly]

Description

I'm using the parse-latex Quarto extension to include LaTeX tables in a book. Here is one example with some context in which I want to refer to that table label

When $\mathbf{\Sigma}$ is the covariance matrix of a multivariate vector $\vec{y}$ with eigenvalues
$\lambda_1 \ge \lambda_2 \ge \dots \lambda_p$,
the properties shown in @tab-eigval-ellipse represent methods of describing the size and shape of the ellipsoid in $\Real{p}$.
More general theory and statistical applications of the geometry of ellispoids is given by
@Friendly-etal:ellipses:2013.

```{=latex}
#| label: tab-eigval-ellipse
\begin{table}[!htb]
\caption{Statistical and geometrical properties of ``size'' of an ellipsoid}\label{tab:ell-size}
\begin{tabular}{llll}
    Size                   &  Conceptual formula                    & Geometry       & Function \\
\hline
(a) Generalized variance:  & $\det{\mathbf{\Sigma}} = \prod_i \lambda_i$ & area, (hyper)volume & geometric mean\\  
(b) Average variance:        & $\text{tr}({\mathbf{\Sigma}}) = \sum_i \lambda_i $ & linear sum & arithmetic mean\\     %% superscripts turned to subscripts / GM
(c) Average precision:        & $1/ \text{tr}({\mathbf{\Sigma}^{-1}}) = 1/\sum_i (1/\lambda_i) $ &  & harmonic mean\\
(d) Maximal variance:      & $\lambda_1$ & maximum dimension & supremum
 \end{tabular}
\end{table}
```

What I get shows the stray #| label I tried to use, and the cross-reference doesn't work. How can I fix that?

[mcanouil]

You don't need anything besides removing the call to the table environment and using the proper prefix for the label.

...
reference to @tbl-eigval-ellipse
...

::: {#tbl-eigval-ellipse tbl-pos="!htb"}
```{=latex}
\begin{tabular}{llll}
    Size                   &  Conceptual formula                    & Geometry       & Function \\
\hline
(a) Generalized variance:  & $\det{\mathbf{\Sigma}} = \prod_i \lambda_i$ & area, (hyper)volume & geometric mean\\  
(b) Average variance:        & $\text{tr}({\mathbf{\Sigma}}) = \sum_i \lambda_i $ & linear sum & arithmetic mean\\     %% superscripts turned to subscripts / GM
(c) Average precision:        & $1/ \text{tr}({\mathbf{\Sigma}^{-1}}) = 1/\sum_i (1/\lambda_i) $ &  & harmonic mean\\
(d) Maximal variance:      & $\lambda_1$ & maximum dimension & supremum
\end{tabular}
```

Statistical and geometrical properties of "size" of an ellipsoid
::: 

parse-latex Quarto extension to include LaTeX tables in a book

What is that? I am not aware of such extension that appears to do what Quarto does natively since its first release.

[friendly]

I'm referring to https://github.com/tarleb/parse-latex

[friendly]

Perfect! Thanks so much

[friendly]

Just for completeness: @mcanouil's answer was missing {llll} The =latex chunk should be:

::: {#tbl-eigval-ellipse tbl-pos="!htb"}
```{=latex}
\begin{tabular}{llll}
    Size                   &  Conceptual formula                    & Geometry       & Function \\
\hline
(a) Generalized variance:  & $\det{\mathbf{\Sigma}} = \prod_i \lambda_i$ & area, (hyper)volume & geometric mean\\  
(b) Average variance:        & $\text{tr}({\mathbf{\Sigma}}) = \sum_i \lambda_i $ & linear sum & arithmetic mean\\     
(c) Average precision:        & $1/ \text{tr}({\mathbf{\Sigma}^{-1}}) = 1/\sum_i (1/\lambda_i) $ &  & harmonic mean\\
(d) Maximal variance:      & $\lambda_1$ & maximum dimension & supremum
\end{tabular}
```

Statistical and geometrical properties of "size" of an ellipsoid
:::

[mcanouil]

Edited my answer to put back this.