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According to John Aldrich's list of "Earliest Uses of Symbols for Matrices and Vectors", the notation $\times$ for direct product goes back to Wedderburn's 1934 Lectures on Matrices (page 74).
Some further search gave a much earlier source, Hurwitz's 1894 Zur Invariantentheorie

I still have to track down the step from $\times$ to $\otimes$.
Incidentally, On the history of the Kronecker product argues that it should more appropriately be called the Zehfuss product.

In any case, since tensor product is $\otimes$ and tensor sum is $\oplus$, it seems obvious that the $\times$ and the $+$ refer to the arithmetical operations of multiplication and addition, not to a letter.

According to John Aldrich's list of "Earliest Uses of Symbols for Matrices and Vectors", the notation $\times$ for direct product (as well as the name itself) goes back to Wedderburn's 1934 Lectures on Matrices (page 74).

Some further search gave a much earlier source, Hurwitz's 1894 Zur Invariantentheorie

I still have to track down the step from $\times$ to $\otimes$.
Incidentally, On the history of the Kronecker product argues that it should more appropriately be called the Zehfuss product.

In any case, since tensor product is $\otimes$ and tensor sum is $\oplus$, it seems obvious that the $\times$ and the $+$ refer to the arithmetical operations of multiplication and addition, not to a letter.

According to John Aldrich's list of "Earliest Uses of Symbols for Matrices and Vectors", the notation $\times$ for direct product goes back to Wedderburn's 1934 Lectures on Matrices (page 74).
Some further search gave a much earlier source, Hurwitz's 1894 Zur Invariantentheorie

I still have to track down the step from $\times$ to $\otimes$.
Incidentally, On the history of the Kronecker product argues that it should more appropriately be called the Zehfuss product.

In any case, since tensor product is $\otimes$ and tensor sum is $\oplus$, it seems obvious that the $\times$ and the $+$ refers to the arithmetical operation of multiplication and addition, not to a letter.

According to John Aldrich's list of "Earliest Uses of Symbols for Matrices and Vectors", the notation $\times$ for direct product goes back to Wedderburn's 1934 Lectures on Matrices (page 74).
Some further search gave a much earlier source, Hurwitz's 1894 Zur Invariantentheorie

I still have to track down the step from $\times$ to $\otimes$.
Incidentally, On the history of the Kronecker product argues that it should more appropriately be called the Zehfuss product.

In any case, since tensor product is $\otimes$ and tensor sum is $\oplus$, it seems obvious that the $\times$ and the $+$ refer to the arithmetical operations of multiplication and addition, not to a letter.

According to John Aldrich's list of "Earliest Uses of Symbols for Matrices and Vectors", the notation $\times$ for direct product goes back to Wedderburn's 1934 Lectures on Matrices (page 74).
Some further search gave a much earlier source, Hurwitz's 1894 Zur Invariantentheorie

I still have to track down the step from $\times$ to $\otimes$.
Incidentally, On the history of the kronecker product argues that it should more appropriately be called the Zehfuss product.

In any case, since tensor product is $\otimes$ and tensor sum is $\oplus$, it seems obvious that the $\times$ and the $+$ refers to the arithmetical operation of multiplication and addition, not to a letter.

According to John Aldrich's list of "Earliest Uses of Symbols for Matrices and Vectors", the notation $\times$ for direct product goes back to Wedderburn's 1934 Lectures on Matrices (page 74).
Some further search gave a much earlier source, Hurwitz's 1894 Zur Invariantentheorie

I still have to track down the step from $\times$ to $\otimes$.
Incidentally, On the history of the Kronecker product argues that it should more appropriately be called the Zehfuss product.

In any case, since tensor product is $\otimes$ and tensor sum is $\oplus$, it seems obvious that the $\times$ and the $+$ refers to the arithmetical operation of multiplication and addition, not to a letter.