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@@ -230,7 +230,7 @@ The \textit{tensor product} of two vectors is defined as follows:
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That is, we take our first vector, multiply the second
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vector by each of its components, and stack the result.
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You could think of this as a generalization of scalar
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multiplication, where scalar multiplication is a
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mulitiplication, where scalar mulitiplication is a
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tensor product with a vector in $\mathbb{R}^1$:
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\begin{equation*}
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a
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@@ -251,7 +251,7 @@ What is it, and what is its color? \par
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\textbf{Part 4:}
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The promoted black bishop on H2 must have been promoted on G1. The pawn which was promoted must have come from G7,
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since neither of the pawns from F6 or H6 could make a capture to get to the G-file (all six missing white pieces have been accounted for).
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since neither of the pawns from F6 or H6 could make a capture to get to the G-file (all six missing white pieces have been accouted for).
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The Pawn from E7 has promoted to the bishop on A2.
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What happened was this: the white pawn from G2 made its capture on H3 while the pawn on G3 was still on H2. This allowed the black pawn
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@@ -331,7 +331,7 @@
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representing all four cubes. \\
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\begin{center} \begin{small}
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\begin{tikzpicture} \label{pic:II_configuration}
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\begin{tikzpicture} \label{pic:II_comfiguration}
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\filldraw [blue] (0,5) -- (1,5) -- (1,6) --
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(0,6) -- (0,5);
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\draw [line width = 1.5pt] (0,5) --
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