Let W be sub-space in dimension m of F^n (m < n). Show that there exist m - n homogeneous equations in n variables, so that- W={(x_1,...x_n) | a_11*x_1+...+a_1n*x_n=0,..., a_n-m*x_1+...+a_n-mn*x_n=0} (x_1,...x_n) is column vector.
Last edited by Also sprach Zarathustra; Dec 30th 2009 at 08:58 AM.
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Originally Posted by Also sprach Zarathustra Let W be sub-space in dimension m of F^n (m < n). Show that there exist m - n homogeneous equations in n variables, so that- W={(x_1,...x_n) | a_11*x_1+...+a_1n*x_n=0,..., a_n-m*x_1+...+a_n-mn*x_n=0} (x_1,...x_n) is column vector. Pick a basis for say and extend to a basis for say we add and take (giving the later a basis ) given by and . We then have and so picking a suitable matrix to represent this we get our equations.
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