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Fix a Typo #26

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Fix a Typo #26

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2 changes: 1 addition & 1 deletion src/diagonalization.xml
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Expand Up @@ -1286,7 +1286,7 @@ The eigenvectors <m>v_1,v_2,v_3</m> are linearly independent: <m>v_1,v_2</m> for
Now suppose that the sum of the geometric multiplicities equals <m>n</m>. As above, this forces the sum of the algebraic multiplicities to equal <m>n</m> as well. As the algebraic multiplicities are all greater than or equal to the geometric multiplicities in any case, this implies that they are in fact equal.
</p>
<p>
Finally, suppose that the third condition is satisfied. Then the sum of the geometric multiplicities equals <m>n</m>. Suppose that the distinct eigenvectors are <m>\lambda_1,\lambda_2,\ldots,\lambda_k</m>, and that <m>\cB_i</m> is a basis for the <m>\lambda_i</m>-eigenspace, which we call <m>V_i</m>. We claim that the collection <m>\cB = \{v_1,v_2,\ldots,v_n\}</m> of all vectors in all of the eigenspace bases <m>\cB_i</m> is linearly independent. Consider the vector equation
Finally, suppose that the third condition is satisfied. Then the sum of the geometric multiplicities equals <m>n</m>. Suppose that the distinct eigenvalues are <m>\lambda_1,\lambda_2,\ldots,\lambda_k</m>, and that <m>\cB_i</m> is a basis for the <m>\lambda_i</m>-eigenspace, which we call <m>V_i</m>. We claim that the collection <m>\cB = \{v_1,v_2,\ldots,v_n\}</m> of all vectors in all of the eigenspace bases <m>\cB_i</m> is linearly independent. Consider the vector equation
<me>
0 = c_1v_1 + c_2v_2 + \cdots + c_nv_n.
</me>
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