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Under "Compatibility with Hadamard products" we have "Vectorization is an algebra homomorphism from the space ..." More specifically, isn't it an isomorphism, and if so should we say this instead? 128.243.253.102 (talk) 15:24, 7 July 2010 (UTC)Reply

In section "Notes" the expression for row-major vectorization looks just as the one in section "Compatibility with Kronecker products". It seems to me that this might not be correct. — Preceding unsigned comment added by \gduld (talk • contribs) 10:06, 27 April 2022 (UTC)Reply

In the section: "Compatibility with Kronecker products", the identity $${\displaystyle \operatorname {vec} (ABC)=(C^{\mathrm {T} }\otimes A)\operatorname {vec} (B)}$$ is introduced, which is true for column-major vectorization. The result in the example relating the vectorization of ${\displaystyle \operatorname {ad} _{A}(X)=AX-XA}$ is not correct assuming the identity from above, since:

$${\displaystyle {\begin{aligned}\operatorname {vec} (\operatorname {ad} _{A}(X))&=\operatorname {vec} (AX-XA)=\operatorname {vec} (AXI_{n}-I_{n}XA)\\&=(I_{n}\otimes A)\operatorname {vec} (X)-(A^{\mathrm {T} }\otimes I_{n})\operatorname {vec} (X)\end{aligned}}}$$

The expression in the article is true using row-based vectorization 89.153.198.117 (talk) 23:47, 9 August 2025 (UTC)Reply