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hank612

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rank(A) ¾ÍÊÇ Image(A)(ÖµÓò)µÄάÊý, Éè Av1,... Avk ÊÇk¸öÏßÐÔÎ޹صÄÒ»×é»ù.

ÄÇô, (BA)v1, ..., (BA)vk Ò»¶¨Éú³É Image(BA), ¿ÉÊÇÕâ k ¸öÏòÁ¿²»±£Ö¤¼ÌÐøÊÇÏßÐÔÎ޹صÄ, ¼´Ò»°ãÀ´Ëµ rank(BA) <= rank(A).

ÌâÄ¿ÖÐ˵ÁË, rank(H)= rank(A), ÄǾÍ˵Ã÷, (BA)v1, ..., (BA)vk »¹ÊÇÏßÐÔÎ޹صÄ, ÕâÒâζ×Å, Èç¹û BAx=0, Ò»¶¨ÓÐ Ax=0. (·ñÔò, ÒÔ Ax ×÷ΪµÚÒ»¸ö»ùÏòÁ¿,À©³ä³ÉImage(A)µÄÒ»×é»ùAv1=Ax,..Avk,  µ«ÊÇBAv1=0,.., BAvk ÓÀÔ¶²»ÊÇImage(BA)µÄÒ»×é»ù.)

Õâ¾ÍÊÇÂ¥Ö÷¹Û²ìµ½µÄ: BºÃÏóÏûʧÁË.
We_must_know. We_will_know.
2Â¥2015-11-20 05:36:37
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_kdh

Òø³æ (ÕýʽдÊÖ)

ÒýÓûØÌû:
2Â¥: Originally posted by hank612 at 2015-11-20 05:36:37
rank(A) ¾ÍÊÇ Image(A)(ÖµÓò)µÄάÊý, Éè Av1,... Avk ÊÇk¸öÏßÐÔÎ޹صÄÒ»×é»ù.

ÄÇô, (BA)v1, ..., (BA)vk Ò»¶¨Éú³É Image(BA), ¿ÉÊÇÕâ k ¸öÏòÁ¿²»±£Ö¤¼ÌÐøÊÇÏßÐÔÎ޹صÄ, ¼´Ò»°ãÀ´Ëµ rank(BA) <= rank(A).
...

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