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## Main Question or Discussion Point

Just as a concrete example, say A and A' are two 2x2 matricies from R^2 to R^2,

[tex]A = \left [ \begin{array}{cc} a \,\, b \\ c \,\, d \end{array} \right ] [/tex]

[tex]A' = \left [ \begin{array}{cc} x \,\, y \\ z \,\, w \end{array} \right ] [/tex]

What would [tex]A \otimes_\mathbb{R} A'[/tex] look like (say wrt the standard basis of [tex]\mathbb{R}^2 \otimes_\mathbb{R} \mathbb{R}^2[/tex]?).

Any help in understanding this would be greatly appreciated.

[tex]A = \left [ \begin{array}{cc} a \,\, b \\ c \,\, d \end{array} \right ] [/tex]

[tex]A' = \left [ \begin{array}{cc} x \,\, y \\ z \,\, w \end{array} \right ] [/tex]

What would [tex]A \otimes_\mathbb{R} A'[/tex] look like (say wrt the standard basis of [tex]\mathbb{R}^2 \otimes_\mathbb{R} \mathbb{R}^2[/tex]?).

Any help in understanding this would be greatly appreciated.