Java Pattern REGEX Where Not Matching

I'm trying to use the Java Pattern and Matcher to apply input checks. I have it working in a really basic format which I am happy with so far. It applies a REGEX to an argument and then loops through the matching characters.

import java.util.regex.Pattern;
import java.util.regex.Matcher;

public class RegexUtil {

   public static void main(String[] args) {

      String    argument;
      Pattern   pattern;
      Matcher   matcher;

      argument = "#a1^b2";
      pattern = Pattern.compile("[a-zA-Z]|[0-9]|\\s");
      matcher = pattern.matcher(argument);

      // find all matching characters
      while(matcher.find()) {
         System.out.println(matcher.group());
      }

   }

}

This is fine for extracting all the good characters, I get the output

a
1
b
2

Now I wanted to know if it's possible to do the same for any characters that don't match the REGEX so I get the output

#
^

Or better yet loop through it and get TRUE or FALSE flags for each index of the argument

false
true
true
false
true
true

I only know how to loop through with matcher.find(), any help would be greatly appreciated