# Why the first principal component is mostly negative while the second component is mostly positive?

I am running PCA for a fleet management data frame $$X$$, where each column is a city, each row is a date, there are 50 cities and 500 dates.

I run PCA on $$A=X^{T}X$$.

Then the first component $$v_{1}$$ is :

$$Av_{1}=\lambda_{1}v_{1}$$

However, I discovered that most of the values in the first component $$v_{1}$$ are negative; while most of the values of the second (and there after till 50) component $$v_{2}$$ are positive.

I am curious to understand from where the negativity comes from. What I understand about PCA is that, the principal components define new axis which are orthogonal to each other. In that case, the sign shouldn't matter, because if I 'flip' the component, it should still be orthogonal to the other components.

If we imagine that the data is projected into a 2-dim space, in my case, the first component is pointing toward the quadrant III;

Or in other words, what does the negative first component say about my input data? Does this imply that input data is skewed (at least , asymmetric) ?