[理工] 線代
1.The set of polynomials of degree n is a subsapce
of the vector space of all polynomials.
(F): why?
2.The set of all m*n matrices with the usual definitions
of matrix addition and scalar multiplication is a
vector space.
(T):this question does not mention the zero subspace contains
in the set,so I think the answer is wrong.
n m
3.The vector space Mm*n and L(R ,R ) are isomorphic.
(T):the definition of isomorphism if the linear transformation
is one-to-one and onto,that is,the standrd representation
matrix is invertibe,which the matrix must be squar.
so I think the answer is wrong.
4.The definite integral is a linear operator on C([a,b]),the
vector space of cotinuous real-valued functions defined on[a,b].
(F):why?
5.If a vector space contains a finite linearly dependent set,then
the vector space is finite-dimesional.
(F):By GSO ,we can get a orthogonal set,which is also linearly
independent set,then this set will be finite(becasue a finite
linearly dependent).
so I think the answer is true.
6.If T is a linear operator on a vector space with the basis
B={v1,v2,...v3},then the matrix representation of T with
respecet to B is the matrix[T(v1) T(v2) ... T(v3)].
(F):If we replace [T(v1) T(v2) ... T(v3)] by
[[T(v1)]B [T(v2)]B ... [T(v3)]B ],then this question
will be true?
7.An inner product on a vector space V is linear operator on V.
(F): why?
8.The indefinite integral can be used to define an inner product
on P2.
(F):why?
n
9.Every subspace of a vector space is a subset of R for some
integer n.
(F): If A is a subspace of B,then A is a subset of B.
so I think the answer is true.
Def: A linear operator on a finite-dimensional vector space is
diagonalizable if there is a basis for the vector space
consisting of eigenvectors of the operator.
我有點不懂這個定義在講什麼= =
問題有點多 感謝板上大大回答
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◆ From: 123.193.7.20
※ 編輯: KAINTS 來自: 123.193.7.20 (08/29 22:52)
推
08/30 00:24, , 1F
08/30 00:24, 1F
→
08/30 00:24, , 2F
08/30 00:24, 2F
推
08/30 00:37, , 3F
08/30 00:37, 3F
→
08/30 00:37, , 4F
08/30 00:37, 4F
→
08/30 00:50, , 5F
08/30 00:50, 5F
→
08/30 00:50, , 6F
08/30 00:50, 6F
推
08/30 00:59, , 7F
08/30 00:59, 7F
→
08/30 01:02, , 8F
08/30 01:02, 8F
可題目有說已經是他的子空間了，我後來想是不是因為這樣
Pn有可能是n+1,n+2,....的子空間
但1,2,...n-1,則不可能，因為題目最後是說all,,所以答案錯
不知道這樣想可以嗎?
→
08/30 01:06, , 9F
08/30 01:06, 9F
推
08/30 01:17, , 10F
08/30 01:17, 10F
→
08/30 01:21, , 11F
08/30 01:21, 11F
意思有點像，內積是做出一個值;linear operator,則是一個矩陣表示，兩者意思不同，
是這樣嗎?
推
08/30 08:29, , 12F
08/30 08:29, 12F
推
08/30 09:33, , 13F
08/30 09:33, 13F
→
08/30 09:36, , 14F
08/30 09:36, 14F
為什麼，不太懂ㄟ...
然後可以問一下，inner product space & vector space,
之間有什麼關聯嗎??
※ 編輯: KAINTS 來自: 111.70.142.103 (08/30 10:00)
※ 編輯: KAINTS 來自: 111.70.142.103 (08/30 10:18)
→
08/30 10:55, , 15F
08/30 10:55, 15F
推
08/30 14:51, , 16F
08/30 14:51, 16F
→
08/30 23:24, , 17F
08/30 23:24, 17F
→
08/30 23:42, , 18F
08/30 23:42, 18F
→
08/30 23:43, , 19F
08/30 23:43, 19F
→
08/30 23:46, , 20F
08/30 23:46, 20F
→
08/30 23:47, , 21F
08/30 23:47, 21F
→
08/30 23:53, , 22F
08/30 23:53, 22F
→
08/30 23:56, , 23F
08/30 23:56, 23F
→
08/30 23:56, , 24F
08/30 23:56, 24F
→
08/31 00:07, , 25F
08/31 00:07, 25F
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