$\pm$ sign in electromagnetic wave ratio of $E$ and $B$ for regressive/progressive case I found on textbook that the magnitude of electric field $E$ and magnetic field $B$ in a plane electromagnetic wave are always related by the fact that
$$\frac{E}{B}=\pm v$$
Where $v$ is the velocity of wave and the $+$ sign is for progressive em wave, while the  $-$ sign is for regressive em wave.
It does not give much explanation for that $\pm$, how should this sign be interpreted?
Since $E$ and $B$ are in phase, they have the same sign in particular, therefore the ratio must be positive, so is the $-$ sign related to the fact that for regressive wave the velocity (component) is negative?
Otherwise, why the $\pm$?
 A: Overview
To my knowledge the terminology "progressive wave" and "regressive wave" is not common, and you can't count on working scientists recognizing it.
This appears to be a scheme to help you workout the relationship between the direction of the fields and the direction of wave propagation; in that it is equivalent to the cross-product
$$ \vec{S} = \vec{E} \times \vec{B} \tag{1} \;,$$
for the Poynting vector. 
Making sense of it
Let's say I know that a plane wave is propagating in free-space along the $z$ axis, but we don't know which way it is going. And that we know the polarization of the wave is such that electric field is along the $x$ axis. 
If—at the time when $\vec{E} = +|E|\hat{x}$—I have


*

*$\vec{B} = +|B|\hat{y}$ then the wave is propagating in the $+\hat{z}$ direction (that is "progressive" in the language above)

*$\vec{B} = -|B|\hat{y}$ then the wave is propagating in the $-\hat{z}$ direction (that is "regressive" in the language above)


In other works, by aligning the ray and fields on the axes we can write $E = E_x(t)$ and $B = B_y(t)$ and the ratio that you exhibit can then have either sign even for a free-space wave that is in-phase.
Suggestion
The relationship is better understood in terms of the cross-product in equation (1) than in the baroque structure offered by the book you are reading. If only because the cross-product is already generalized to non-axis-aligned propagation.
A: This would be true only for propagation in lossless media.  Moreover, since we are discussing magnitudes the $-$ sign does not make sense.
In general the ratio $E/H$ is related to the impedance $\eta$ of the medium in which the wave propagates.  This impedance is complex in general but real for lossless media (for which the conductivity $\sigma=0$.)  When $\eta$ is complex, $\vec E$ and $\vec H$ need not be in phase: the maxima of $E$ and $H$ are shifted, with the shift related to the argument of $\eta$, but this phase-shift is time-independent.
For propagation in a lossless medium we have
$$
H=\frac{E}{\eta}=\frac{B}{\mu}\, .
$$
In vacuum $\eta=\sqrt{\mu_0/\epsilon_0}\approx 377\Omega$ and $\mu=\mu_0=4\pi\times 10^{-7}$.  Thus
$$
\frac{E}{B}=\frac{\eta_0}{\mu_0}=\frac{1}{\sqrt{\mu_0\epsilon_0}}=c
$$
which would generalize to $v=1/\sqrt{\mu\epsilon}$ for another lossless medium.
