Difference between revisions of "12-240/Classnotes for Tuesday October 09"
From Drorbn
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== theorems == | == theorems == | ||
+ | 1/ β is a basic of V iff every element of V can be written as a linear combination of elements of β in a unique way. | ||
+ | proof: ( in the case β is finite) | ||
+ | |||
+ | β = {u1, u2, ..., un} | ||
+ | |||
+ | (<=) need to show that β = span(V) and β is linearly independent. | ||
== Lecture notes scanned by [[User:Oguzhancan|Oguzhancan]] == | == Lecture notes scanned by [[User:Oguzhancan|Oguzhancan]] == |
Revision as of 16:38, 12 October 2012
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In this lecture, the professor concentrate on basics and related theorems.
Definition of basic
β V is a basic if
1/ It generates ( span) V, span β = V
2/ It is linearly independent
theorems
1/ β is a basic of V iff every element of V can be written as a linear combination of elements of β in a unique way.
proof: ( in the case β is finite)
β = {u1, u2, ..., un}
(<=) need to show that β = span(V) and β is linearly independent.