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#1
09 ÁԶعÒ¹ 2015, 15:05
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Linear Transformation
Let $V$ be a finite dimensional vector space over a field $F$ and Let $ T : V \rightarrow V$ be a linear transformation. Suppose that $ V = im(T) + ker(T)$ , prove that $V$ is a direct sum of $im(T)$ and $ker(T)$. Give a counterexample of the above assertion when $V$ is infinite dimensional
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| Êͺ¶ÒÁàÃ×èͧ linear transformation ¤ÃѺ | Anupon | ¤³ÔµÈÒʵÃìÍØ´ÁÈÖ¡ÉÒ | 4 | 16 ¡Ñ¹ÂÒ¹ 2014 13:13 |
| Linear transformation ¤Ñº | Tohn | ¤³ÔµÈÒʵÃìÍØ´ÁÈÖ¡ÉÒ | 6 | 06 ¡Ñ¹ÂÒ¹ 2012 21:26 |
| Algebra : linear transformation | B º .... | ¾Õª¤³Ôµ | 6 | 18 ÊÔ§ËÒ¤Á 2012 10:28 |
| ¶ÒÁà¡ÕèÂǡѺ Linear transformation ¤èÐ | khlongez | ¤³ÔµÈÒʵÃìÍØ´ÁÈÖ¡ÉÒ | 3 | 21 ¡ØÁÀҾѹ¸ì 2012 17:32 |
| transformation matrix | kryly | »ÑËÒ¤³ÔµÈÒʵÃì·ÑèÇä» | 3 | 31 ¸Ñ¹ÇÒ¤Á 2011 17:24 |
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