plural bases
                                        ˈbā-ˌsēz 
    
            
        
    1
                    
                                          
              
          
                                                      : the bottom of something considered as its foundation                                      
                
                    
2
                    
                                          
              
          
                                                      : the principal component of something                                      
              
                             
Fruit juice constitutes the basis of jelly.
                         
                
                    3
                    
        a
    
          
                                          
              
          
                                                      : something on which something else is established or based                                      
              
                             
stories with little basis in reality
                                       no legal basis for a new trial
                                       still some basis for hope
                                       selected on the basis of test scores
                         
                
                    
        b
    
          
                                          
              
          
                                                      : an underlying condition or state of affairs                                      
              
                             
hired on a trial basis
                                       He is on a first-name basis with his customers.
                         
                
                    
        c
    
          
                                          
              
          
                                                      : a fixed pattern or system                                      
              
                             
meets with us on a regular basis [=regularly]
                                       The department sends reports on a daily basis. [=every day]
                         
                
                    4
                    
                                          
              
          
                                                      : the basic principle                                      
              
                             
concepts that form the basis of the country's economic policies
                         
                
                    5
                    
                                mathematics 
                                  
              
          
                                                      : a set of linearly independent vectors (see vector entry 1 sense 1a) in a vector space such that any vector in the vector space can be expressed as a linear combination of them with appropriately chosen coefficients (see coefficient sense 1)                                      
                
                    
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  Merriam-Webster unabridged




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