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| The kernels <math>\varphi_{\mathbf{x}_1}, \varphi_{\mathbf{x}_2}, \dots, \varphi_{\mathbf{x}_n}</math> are linearly independent (for example <math>\varphi(r)=r^2</math> in <math>V=\mathbb{R}</math> is not a radial basis function)
| The kernels <math>\varphi_{\mathbf{x}_1}, \varphi_{\mathbf{x}_2}, \dots, \varphi_{\mathbf{x}_n}</math> form a basis for a [[Haar space|Haar Space]], meaning that the [[radial basis function interpolation|interpolation matrix]] (given below) is non-[[singular matrix|singular]].<ref>{{cite book |last1=Fasshauer |first1=Gregory E. |title=Meshfree Approximation Methods with MATLAB |date=2007 |publisher=World Scientific Publishing Co. Pte. Ltd. |___location=Singapore |isbn=9789812706331 |pages=17–25}}</ref><ref name="wendland2005">{{cite book |last1=Wendland |first1=Holger |title=Scattered Data Approximation |date=2005 |publisher=Cambridge University Press |___location=Cambridge |isbn=0521843359 |pages=11, 18-23,64-66}}</ref>
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