Hexagonal water, alkaline ionized water I am chemical engineering and i care my nutrition and health. in my opinion, it is so important that what we drink or eat daily.
 Respectfully, I have a question about alkaline ionized water bottle, Which is sold commercially. I have some information about production of electrolyzed water technology. as i study in some articles, hard water (water with minerals such as calcium bicarbonate) electrolyzed in a electrolysis cell and Hydroxide is produced. As i knew, calcium and magnesium hydroxide are insoluble in water. But we don't see any white residue in commercial alkaline ionized water bottle. These particles (as an alkaline agents) are probably filtered, my question is " if calcium and magnesium hydroxide are filtered, why this water have pH 9 or high??"
thank you
I'd be happy and it is my pleasure if you tell me this.
As Waylander states, calcium and magnesium hydroxides do have some solubility in water.  In the case of magnesium hydroxide you can demonstrate this by simply buying some milk of magnesia and applying red litmus paper to it; the paper turns blue like there were an alkali.

Simply dissolving either calcium or magnesium hydroxide into water would raise the pH beyond the target (you get 10 for magnesium, 12 for calcium).  Additional calcium or magnesium salts may be introduced to shift the dissolution equilibrium for the sparingly soluble hydroxide, and thus control the pH.

Here and here the use of lime and magnesia for water treatment is mentioned.  Both work by making the water slightly alkaline so as to displace heavy metals as less soluble hydroxides.