当前位置:网站首页>"Hands on learning in depth" Chapter 2 - preparatory knowledge_ 2.3 linear algebra_ Learning thinking and exercise answers
"Hands on learning in depth" Chapter 2 - preparatory knowledge_ 2.3 linear algebra_ Learning thinking and exercise answers
2022-07-06 02:31:00 【coder_ sure】
List of articles
2.3 linear algebra
author github link : github link
practice
- Prove a matrix A \mathbf{A} A The transpose of is A \mathbf{A} A, namely ( A ⊤ ) ⊤ = A (\mathbf{A}^\top)^\top = \mathbf{A} (A⊤)⊤=A.
- Two matrices are given A \mathbf{A} A and B \mathbf{B} B, prove “ They are transposed and ” be equal to “ They are transposed with ”, namely A ⊤ + B ⊤ = ( A + B ) ⊤ \mathbf{A}^\top + \mathbf{B}^\top = (\mathbf{A} + \mathbf{B})^\top A⊤+B⊤=(A+B)⊤.
- Given an arbitrary square matrix A \mathbf{A} A, A + A ⊤ \mathbf{A} + \mathbf{A}^\top A+A⊤ Is it always symmetrical ? Why? ?
- We define shapes in this section ( 2 , 3 , 4 ) (2,3,4) (2,3,4) Tensor
X
.len(X)
What is the output of ? - For tensors of arbitrary shape
X
,len(X)
Whether it always corresponds toX
The length of a particular axis ? What is this axis ? - function
A/A.sum(axis=1)
, See what happens . Can you analyze the reason ? - Consider a with a shape ( 2 , 3 , 4 ) (2,3,4) (2,3,4) Tensor , In the shaft 0、1、2 What shape is the summation output on ?
- by
linalg.norm
Function provides 3 Tensors of one or more axes , And observe its output . For tensors of any shape, what does this function calculate ?
Practice reference answers ( If there is a mistake , Please also correct )
1. Prove a matrix A \mathbf{A} A The transpose of is A \mathbf{A} A, namely ( A ⊤ ) ⊤ = A (\mathbf{A}^\top)^\top = \mathbf{A} (A⊤)⊤=A.
A·=·torch.arange(12).reshape(3,4)A,(A.T).T
output:
(tensor([[ 0, 1, 2, 3],
[ 4, 5, 6, 7],
[ 8, 9, 10, 11]]), tensor([[ 0, 1, 2, 3],
[ 4, 5, 6, 7],
[ 8, 9, 10, 11]]))
2. Two matrices are given A \mathbf{A} A and B \mathbf{B} B, prove “ They are transposed and ” be equal to “ They are transposed with ”, namely A ⊤ + B ⊤ = ( A + B ) ⊤ \mathbf{A}^\top + \mathbf{B}^\top = (\mathbf{A} + \mathbf{B})^\top A⊤+B⊤=(A+B)⊤.
B = torch.tensor([[9, 8, 7,6], [5, 4, 3,2], [3, 4, 5,1]])
A.T+B.T ,(A+B).T
output:
(tensor([[ 9, 9, 11],
[ 9, 9, 13],
[ 9, 9, 15],
[ 9, 9, 12]]), tensor([[ 9, 9, 11],
[ 9, 9, 13],
[ 9, 9, 15],
[ 9, 9, 12]]))
3. Given an arbitrary square matrix A \mathbf{A} A, A + A ⊤ \mathbf{A} + \mathbf{A}^\top A+A⊤ Is it always symmetrical ? Why? ?
answer : because ( A + A ⊤ ) ⊤ = A ⊤ + A = A + A ⊤ (\mathbf{A} + \mathbf{A}^\top)^\top=\mathbf{A}^\top+\mathbf{A}=\mathbf{A} + \mathbf{A}^\top (A+A⊤)⊤=A⊤+A=A+A⊤
A = torch.arange(9).reshape(3,3)
A
output:
tensor([[0, 1, 2],
[3, 4, 5],
[6, 7, 8]])
A+A.T
output:
tensor([[ 0, 4, 8],
[ 4, 8, 12],
[ 8, 12, 16]])
4. We define shapes in this section ( 2 , 3 , 4 ) (2,3,4) (2,3,4) Tensor X
.len(X)
What is the output of ?
X = torch.arange(24).reshape(2, 3, 4)
len(X)
output:
2
5. For tensors of arbitrary shape X
,len(X)
Whether it always corresponds to X
The length of a particular axis ? What is this axis ?
answer :len(X) Total correspondence No 0 Length of shaft .
6. function A/A.sum(axis=1)
, See what happens . Can you analyze the reason ?
answer : Unable to run , as a result of A It's a 5 * 4 Matrix , and A.sum(axis=1) It's a flattened 1 Dimension vector , The two dimensions do not match and cannot be divided .( notes : Broadcasting can only happen when the two dimensions are the same , For example, they are all two-dimensional )
A = torch.arange(20, dtype=torch.float32).reshape(5, 4)
A/A.sum(axis=1,keepdims=True)
output:
tensor([[0.0000, 0.1667, 0.3333, 0.5000],
[0.1818, 0.2273, 0.2727, 0.3182],
[0.2105, 0.2368, 0.2632, 0.2895],
[0.2222, 0.2407, 0.2593, 0.2778],
[0.2286, 0.2429, 0.2571, 0.2714]])
A = torch.arange(20, dtype=torch.float32).reshape(5, 4)
A/A.sum(axis=1)
output:
---------------------------------------------------------------------------
RuntimeError Traceback (most recent call last)
<ipython-input-59-86c8759e15d3> in <module>()
1 A = torch.arange(20, dtype=torch.float32).reshape(5, 4)
----> 2 A/A.sum(axis=1)
RuntimeError: The size of tensor a (4) must match the size of tensor b (5) at non-singleton dimension 1
7. Consider a with a shape ( 2 , 3 , 4 ) (2,3,4) (2,3,4) Tensor , In the shaft 0、1、2 What shape is the summation output on ?
H=torch.arange(24).reshape(2,3,4)
H
output:
tensor([[[ 0, 1, 2, 3],
[ 4, 5, 6, 7],
[ 8, 9, 10, 11]],
[[12, 13, 14, 15],
[16, 17, 18, 19],
[20, 21, 22, 23]]])
H0 = H.sum(axis=0)
H1 = H.sum(axis=1)
H2 = H.sum(axis=2)
H0, H1, H2
output:
(tensor([[12, 14, 16, 18],
[20, 22, 24, 26],
[28, 30, 32, 34]]), tensor([[12, 15, 18, 21],
[48, 51, 54, 57]]), tensor([[ 6, 22, 38],
[54, 70, 86]]))
8. by linalg.norm
Function provides 3 Tensors of one or more axes , And observe its output . For tensors of any shape, what does this function calculate ?
answer : In fact, it is the operation of finding norms ( The default is 2 norm )
Z=torch.ones(2,3,4)
W=torch.ones(2,2,3,4)
torch.norm(Z)*torch.norm(Z),torch.norm(W)*torch.norm(W)
output:
(tensor(24.0000), tensor(48.))
边栏推荐
- Li Kou today's question -729 My schedule I
- I changed the driver to 5.1.35, but it is still the same error. I can succeed even now, but I will report this every time I do an SQL operation
- Ue4- how to make a simple TPS role (II) - realize the basic movement of the role
- Exness: Mercedes Benz's profits exceed expectations, and it is predicted that there will be a supply chain shortage in 2022
- [Yunju entrepreneurial foundation notes] Chapter II entrepreneur test 14
- What should we pay attention to when using the built-in tool to check the health status in gbase 8C database?
- Minecraft 1.16.5 生化8 模组 2.0版本 故事书+更多枪械
- 更改对象属性的方法
- 0211 embedded C language learning
- Concept of storage engine
猜你喜欢
High number_ Vector algebra_ Unit vector_ Angle between vector and coordinate axis
[Yunju entrepreneurial foundation notes] Chapter II entrepreneur test 7
The ECU of 21 Audi q5l 45tfsi brushes is upgraded to master special adjustment, and the horsepower is safely and stably increased to 305 horsepower
The ECU of 21 Audi q5l 45tfsi brushes is upgraded to master special adjustment, and the horsepower is safely and stably increased to 305 horsepower
Black high-end responsive website dream weaving template (adaptive mobile terminal)
The third level of C language punch in
[solution] every time idea starts, it will build project
好用的 JS 脚本
Easy to use js script
2022 eye health exhibition, vision rehabilitation exhibition, optometry equipment exhibition, eye care products exhibition, eye mask Exhibition
随机推荐
HDU_ p1237_ Simple calculator_ stack
0211 embedded C language learning
[Digital IC manual tearing code] Verilog asynchronous reset synchronous release | topic | principle | design | simulation
Compact lidar global and Chinese markets 2022-2028: technology, participants, trends, market size and share Research Report
好用的 JS 脚本
729. My schedule I / offer II 106 Bipartite graph
【无标题】数据库中一条查询SQL执行的过程
[Yunju entrepreneurial foundation notes] Chapter II entrepreneur test 11
Thinking on Architecture Design (under continuous updating)
MySQL winter vacation self-study 2022 11 (6)
[Yunju entrepreneurial foundation notes] Chapter II entrepreneur test 10
Spark accumulator
有没有sqlcdc监控多张表 再关联后 sink到另外一张表的案例啊?全部在 mysql中操作
【coppeliasim】6自由度路径规划
Ue4- how to make a simple TPS role (II) - realize the basic movement of the role
Prepare for the autumn face-to-face test questions
[Yunju entrepreneurial foundation notes] Chapter II entrepreneur test 16
【MySQL 15】Could not increase number of max_open_files to more than 10000 (request: 65535)
2020.02.11
550 permission denied occurs when FTP uploads files, which is not a user permission problem