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I just began studying QM on Sakurai's "Modern Quantum Mechanics" and just finished chapter 1. I am now approaching the exercises. On exercise 2 there is a notation I can't understand: "A 2x2 square matrix X is written as X = a_0 + s · a", with a_0 and a_1,2,3 numbers" (s is sigma actually). I can't understand this notation: it is clear that s and a are vectors with the same dimensionality, and a = a_1, a_2, a_3 so I guess s = s_1, s_2, s_3. How can their product produce a 2x2 matrix? And What kind of product does Sakurai intend with s · a? (I used a_0 to mean a with 0 subscript) Thanks

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  • $\begingroup$ s are the pauli matrices. Each s_i is a 2 by 2 Matrix. The identity 2x2 Matrix is implicit with the a_0. $\endgroup$ – lalala May 31 at 9:26
  • $\begingroup$ Oh, this is an epiphany! (Even though, in the chapter text it is generally explicited when eye is implicit). But given what you said, there is som sum implicit in s · a or the X operator is a set of 3 operators? And if so, why isn't it fomatted as bold? $\endgroup$ – Dario Ligori May 31 at 9:32
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    $\begingroup$ Please use Mathjax for mathematics expressions and variables. It is the site standard. $\endgroup$ – StephenG May 31 at 9:34
  • $\begingroup$ There is no X in your Question, so not sure. sigma consists of three Matrices. And then a dot s is meant as a_1 s_1+a_2s_2+ a_3 s_3. Why the formatting is different then expected, we have to ask the Editor of the book. $\endgroup$ – lalala May 31 at 9:35
  • $\begingroup$ Thanks all, sorry for unexperience about expression coding, I'll use next time. $\endgroup$ – Dario Ligori May 31 at 9:41

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