<p dir="auto">In Julia &gt;1.0 I observed the product between a real and a complex matrix run very slowly. This does not concern the complex and real matrix product however:</p>
<div class="snippet-clipboard-content notranslate position-relative overflow-auto" data-snippet-clipboard-copy-content="M = 2000
C = rand(M,M) + im*rand(M,M)
R = rand(M,M)
@time C * R;
@time R * C;

  0.090447 seconds (11 allocations: 61.036 MiB, 2.09% gc time)
  6.074982 seconds (12 allocations: 61.036 MiB, 0.61% gc time)"><pre class="notranslate"><code class="notranslate">M = 2000
C = rand(M,M) + im*rand(M,M)
R = rand(M,M)
@time C * R;
@time R * C;

  0.090447 seconds (11 allocations: 61.036 MiB, 2.09% gc time)
  6.074982 seconds (12 allocations: 61.036 MiB, 0.61% gc time)
</code></pre></div>
<p dir="auto">Julia 0.4:<br>
julia&gt; A=rand(3000,3000);B=rand(3000,3000);<br>
julia&gt; tic();for k=1:50;C=A.*B;end;toc()<br>
elapsed time: 2.386786733 seconds<br>
2.386786733</p>
<p dir="auto">Matlab 2013a:</p>
<blockquote>
<blockquote>
<p dir="auto">A=rand(3000);B=rand(3000);<br>
tic;for k=1:50;C=A.*B;end;toc<br>
Elapsed time is 1.501691 seconds.</p>
</blockquote>
</blockquote>
<p dir="auto">This is on a 2 core machine. I also ran it on another computer with 6 cores and the difference is greater (about 4x). So it seems Matlab is using parallelism for .* while Julia isn't. A little experimentation in Matlab shows that it drops to 1 core when the matrix size is 191x191 or smaller.</p>