Using phantom in align environment

[Dustinsfl]

The extra align row at the top contributes a lot of white space but I need phantom equal at spacing of a previous align above it. How can I keep the spacing but remove the white space gap?

\begin{alignat*}{3}
\phantom{\sigma_1:} & \phantom{\begin{bmatrix}
3 - \sigma_1 & -10 & 0\\
-10 & 0 - \sigma_1 & 30\\
0 & 30 & -27 - \sigma_1
\end{bmatrix}} & \phantom{=} &\phantom{\begin{bmatrix}
3 + 47 & -10 & 0\\
-10 & 47 & 30\\
0 & 30 & -27 + 47
\end{bmatrix}}\\
\sigma_3: & \begin{bmatrix}
3 - \sigma_3 & -10 & 0\\
-10 & 0 - \sigma_3 & 30\\
0 & 30 & -27 - \sigma_3
\end{bmatrix} & = & \begin{bmatrix}
3 - 23 & -10 & 0\\
-10 & -23 & 30\\
0 & 30 & -27 - 23
\end{bmatrix}\\
 & & = & \begin{bmatrix}
-20 & -10 & 0\\
-10 & -23 & 30\\
0 & 30 & -50
\end{bmatrix}\\
 & & = & \begin{bmatrix}
-2 & -1 & 0\\
-10 & -23 & 30\\
0 & 3 & -5
\end{bmatrix}\\
 & & = & \begin{bmatrix}
-2 & -1 & 0\\
0 & -18 & 30\\
0 & 3 & -5
\end{bmatrix}\\
 & & = & \begin{bmatrix}
-2 & -1 & 0\\
0 & -3 & 5\\
0 & 3 & -5
\end{bmatrix}\\
 & & = & \begin{bmatrix}
-2 & -1 & 0\\
0 & -3 & 5\\
0 & 0 & 0
\end{bmatrix}\\
\end{alignat*}

 

[Opalg]

I would use the aligned environment rather than alignat*.

\begin{aligned}
\sigma_3: \begin{bmatrix}3 - \sigma_3 & -10 & 0 \\-10 & 0 - \sigma_3 & 30 \\ 0 & 30 & -27 - \sigma_3 \end{bmatrix} 
& = \begin{bmatrix}3 - 23 & -10 & 0 \\-10 & -23 & 30 \\0 & 30 & -27 - 23\end{bmatrix} \\ 
& = \begin{bmatrix}-20 & -10 & 0 \\-10 & -23 & 30 \\0 & 30 & -50\end{bmatrix} \\ 
& = \begin{bmatrix}-2 & -1 & 0 \\-10 & -23 & 30 \\0 & 3 & -5\end{bmatrix} \\
& = \begin{bmatrix}-2 & -1 & 0 \\0 & -18 & 30 \\0 & 3 & -5\end{bmatrix} \\
& = \begin{bmatrix}-2 & -1 & 0 \\0 & -3 & 5 \\0 & 3 & -5\end{bmatrix} \\
& = \begin{bmatrix}-2 & -1 & 0 \\0 & -3 & 5 \\0 & 0 & 0\end{bmatrix} \\ 
\end{aligned}

That produces $$\begin{aligned}\sigma_3: \begin{bmatrix}3 - \sigma_3 & -10 & 0 \\-10 & 0 - \sigma_3 & 30 \\ 0 & 30 & -27 - \sigma_3
\end{bmatrix} & = \begin{bmatrix}3 - 23 & -10 & 0 \\-10 & -23 & 30 \\0 & 30 & -27 - 23\end{bmatrix} \\ & = \begin{bmatrix}-20 & -10 & 0 \\-10 & -23 & 30 \\0 & 30 & -50\end{bmatrix} \\ & = \begin{bmatrix}-2 & -1 & 0 \\-10 & -23 & 30 \\0 & 3 & -5\end{bmatrix} \\& = \begin{bmatrix}-2 & -1 & 0 \\0 & -18 & 30 \\0 & 3 & -5\end{bmatrix} \\& = \begin{bmatrix}-2 & -1 & 0 \\0 & -3 & 5 \\0 & 3 & -5\end{bmatrix} \\& = \begin{bmatrix}-2 & -1 & 0 \\0 & -3 & 5 \\0 & 0 & 0\end{bmatrix} \\ \end{aligned}$$

Edit. If you want the left side of the top row to occupy the same space as $\sigma_1: \begin{bmatrix}3 - \sigma_1 & -10 & 0 \\ -10 & 0 - \sigma_1 & 30\\0 & 30 & -27 - \sigma_1 \end{bmatrix}$ then (in the above code) you can replace

\sigma_3: \begin{bmatrix}3 - \sigma_3 & -10 & 0 \\-10 & 0 - \sigma_3 & 30 \\ 0 & 30 & -27 - \sigma_3 \end{bmatrix}

by

\phantom{\sigma_1: \begin{bmatrix}3 - \sigma_1 & -10 & 0 \\-10 & 0 - \sigma_1 & 30 \\0 & 30 & -27 - \sigma_1 \end{bmatrix}}
 \llap{$\sigma_3: \begin{bmatrix}3 - \sigma_3 & -10 & 0 \\-10 & 0 - \sigma_3 & 30 \\ 0 & 30 & -27 - \sigma_3 \end{bmatrix}$}

That material will be aligned close to the $=$ sign, without unwanted white space.

 

[Dustinsfl]

I would use the aligned environment rather than alignat*.

\begin{aligned}
\sigma_3: \begin{bmatrix}3 - \sigma_3 & -10 & 0 \\-10 & 0 - \sigma_3 & 30 \\ 0 & 30 & -27 - \sigma_3 \end{bmatrix} 
& = \begin{bmatrix}3 - 23 & -10 & 0 \\-10 & -23 & 30 \\0 & 30 & -27 - 23\end{bmatrix} \\ 
& = \begin{bmatrix}-20 & -10 & 0 \\-10 & -23 & 30 \\0 & 30 & -50\end{bmatrix} \\ 
& = \begin{bmatrix}-2 & -1 & 0 \\-10 & -23 & 30 \\0 & 3 & -5\end{bmatrix} \\
& = \begin{bmatrix}-2 & -1 & 0 \\0 & -18 & 30 \\0 & 3 & -5\end{bmatrix} \\
& = \begin{bmatrix}-2 & -1 & 0 \\0 & -3 & 5 \\0 & 3 & -5\end{bmatrix} \\
& = \begin{bmatrix}-2 & -1 & 0 \\0 & -3 & 5 \\0 & 0 & 0\end{bmatrix} \\ 
\end{aligned}

That produces $$\begin{aligned}\sigma_3: \begin{bmatrix}3 - \sigma_3 & -10 & 0 \\-10 & 0 - \sigma_3 & 30 \\ 0 & 30 & -27 - \sigma_3
\end{bmatrix} & = \begin{bmatrix}3 - 23 & -10 & 0 \\-10 & -23 & 30 \\0 & 30 & -27 - 23\end{bmatrix} \\ & = \begin{bmatrix}-20 & -10 & 0 \\-10 & -23 & 30 \\0 & 30 & -50\end{bmatrix} \\ & = \begin{bmatrix}-2 & -1 & 0 \\-10 & -23 & 30 \\0 & 3 & -5\end{bmatrix} \\& = \begin{bmatrix}-2 & -1 & 0 \\0 & -18 & 30 \\0 & 3 & -5\end{bmatrix} \\& = \begin{bmatrix}-2 & -1 & 0 \\0 & -3 & 5 \\0 & 3 & -5\end{bmatrix} \\& = \begin{bmatrix}-2 & -1 & 0 \\0 & -3 & 5 \\0 & 0 & 0\end{bmatrix} \\ \end{aligned}$$

Edit. If you want the left side of the top row to occupy the same space as $\sigma_1: \begin{bmatrix}3 - \sigma_1 & -10 & 0 \\ -10 & 0 - \sigma_1 & 30\\0 & 30 & -27 - \sigma_1 \end{bmatrix}$ then (in the above code) you can replace

\sigma_3: \begin{bmatrix}3 - \sigma_3 & -10 & 0 \\-10 & 0 - \sigma_3 & 30 \\ 0 & 30 & -27 - \sigma_3 \end{bmatrix}

by

\phantom{\sigma_1: \begin{bmatrix}3 - \sigma_1 & -10 & 0 \\-10 & 0 - \sigma_1 & 30 \\0 & 30 & -27 - \sigma_1 \end{bmatrix}}
 \llap{$\sigma_3: \begin{bmatrix}3 - \sigma_3 & -10 & 0 \\-10 & 0 - \sigma_3 & 30 \\ 0 & 30 & -27 - \sigma_3 \end{bmatrix}$}

That material will be aligned close to the $=$ sign, without unwanted white space.

Thanks it did remove the white space, but it doesn't align correct then with the align environment above it.

 

[Ackbach]

The tabbing environment provides more direct control over where things align, and you can make them consistent even when interrupted by text in-between environments. See http://www.mathhelpboards.com/f26/possibly-tricky-alignment-problem-1493/. Also see http://www.mathhelpboards.com/f26/align*-environment-inside-tabbing-environment-2150/.

 

[alphy]

If you need to keep the spacing of the previous align environment but want to remove the extra white space, you can use the \vphantom command instead of \phantom. This will create an invisible vertical space that will maintain the spacing without adding any visible elements. Alternatively, you can use \smash to remove the vertical space altogether, but this may affect the alignment of your equations. It is important to note that using \phantom or \vphantom may also affect the spacing of your equations if they contain elements such as fractions or exponents, so it is important to test and adjust accordingly.