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I'm reading my old notes of QM, I found the definition of Pauli vector, as follow

[tex]\vec{\sigma}=\sigma_1 e_x+\sigma_2e_y + \sigma_3 e_z[/tex]

Where [tex]e_x. e_y[/tex] and [tex]e_z[/tex] are unit vectors.

So, here is my question. [tex]\sigma_i[/tex] and [tex]e_i[/tex] are elements of different nature. How can we define the product [tex]\sigma_ie_i[/tex]??

I understand the idea, ok. But, mathematically don't seem right

Thanks in advance