Confusion in Lorentz Boost Equations: Minus Sign Needed?

[facenian]

On page 29 equations 2.1.20 and 2.1.21 of Gravitation and Cosmology by S. Weinberg he gives these expresions for matrix componentes:
$$\Lambda_j^0=\gamma v_j$$
My question is: shouldn't there be a minus sign on left side of the equation?

 

[Phrak]

By looking at your latex source you seem to be writing

$${\Lambda_j}^0 = \gamma v_j$$
Now, I don't know Weinberg's convension for index placement for a Lorentz vs. inverse Lorentz transform matrices. Different authors use different convensions.

However, the positive sign of $\gamma v_j$ indicates that it must be an inverse Lorentz transform if $v_j$ is taken to be directed in the usual manner.

On the other hand, authors make typos and mistakes and proof readers don't catch them all. Just tonight, I'm reading some gr lecture notes by G. 't Hooft (nephew of G. 't Hooft, it seems), and it's peppered with plenty of them.

 

[Bill_K]

Weinberg: "Suppose that one observer O sees a particle at rest, and a second observer O' sees it moving with velocity v."

In other words, he's saying that the line x = 0 corresponds to x' = vt'. This is the opposite of what most treatments assume, namely that x' = 0 corresponds to x = vt. So his definition of v is the opposite.

 

[facenian]

thank you both for your comments.
I understood the way Bill K says, but I needed a confirmation. I think we can replace v by minus -v only if both frames are parallel getting in this way the ussual form of the transformation equations.