Skip to content

Navigation Menu

Sign in
Appearance settings

Search code, repositories, users, issues, pull requests...

Provide feedback

We read every piece of feedback, and take your input very seriously.

Saved searches

Use saved searches to filter your results more quickly
Sign up
Appearance settings

Commit 591761d

Browse files
Add files via upload
1 parent 2edae1e commit 591761d

File tree

1 file changed

+353
-0
lines changed

1 file changed

+353
-0
lines changed

‎9. Linear Algebra.ipynb

Lines changed: 353 additions & 0 deletions
Original file line numberDiff line numberDiff line change
@@ -0,0 +1,353 @@
1+
{
2+
"cells": [
3+
{
4+
"cell_type": "markdown",
5+
"metadata": {},
6+
"source": [
7+
"#### Linear Algebra\n",
8+
"Work in progress. Basic linear algebra to be included here."
9+
]
10+
},
11+
{
12+
"cell_type": "markdown",
13+
"metadata": {},
14+
"source": [
15+
"#### Simple Array Operations"
16+
]
17+
},
18+
{
19+
"cell_type": "code",
20+
"execution_count": 1,
21+
"metadata": {},
22+
"outputs": [],
23+
"source": [
24+
"import numpy as np"
25+
]
26+
},
27+
{
28+
"cell_type": "code",
29+
"execution_count": 2,
30+
"metadata": {},
31+
"outputs": [
32+
{
33+
"data": {
34+
"text/plain": [
35+
"array([[1., 2.],\n",
36+
" [3., 4.]])"
37+
]
38+
},
39+
"execution_count": 2,
40+
"metadata": {},
41+
"output_type": "execute_result"
42+
}
43+
],
44+
"source": [
45+
"a = np.array([[1.0, 2.0], [3.0, 4.0]])\n",
46+
"a"
47+
]
48+
},
49+
{
50+
"cell_type": "code",
51+
"execution_count": 3,
52+
"metadata": {},
53+
"outputs": [
54+
{
55+
"data": {
56+
"text/plain": [
57+
"array([[1., 3.],\n",
58+
" [2., 4.]])"
59+
]
60+
},
61+
"execution_count": 3,
62+
"metadata": {},
63+
"output_type": "execute_result"
64+
}
65+
],
66+
"source": [
67+
"a.transpose()"
68+
]
69+
},
70+
{
71+
"cell_type": "code",
72+
"execution_count": 4,
73+
"metadata": {},
74+
"outputs": [
75+
{
76+
"data": {
77+
"text/plain": [
78+
"array([[1., 3.],\n",
79+
" [2., 4.]])"
80+
]
81+
},
82+
"execution_count": 4,
83+
"metadata": {},
84+
"output_type": "execute_result"
85+
}
86+
],
87+
"source": [
88+
"a.T"
89+
]
90+
},
91+
{
92+
"cell_type": "code",
93+
"execution_count": 12,
94+
"metadata": {},
95+
"outputs": [
96+
{
97+
"data": {
98+
"text/plain": [
99+
"array([[ 0.6, -0.7],\n",
100+
" [-0.2, 0.4]])"
101+
]
102+
},
103+
"execution_count": 12,
104+
"metadata": {},
105+
"output_type": "execute_result"
106+
}
107+
],
108+
"source": [
109+
"np.linalg.inv(a)"
110+
]
111+
},
112+
{
113+
"cell_type": "code",
114+
"execution_count": 13,
115+
"metadata": {},
116+
"outputs": [],
117+
"source": [
118+
"from numpy.linalg import inv\n",
119+
"a = np.array([[4,7], [2, 6]])\n",
120+
"ainv = inv(a)"
121+
]
122+
},
123+
{
124+
"cell_type": "markdown",
125+
"metadata": {},
126+
"source": [
127+
"![](https://lh3.googleusercontent.com/-KJ2ZOE9awz4/XTfHDTssSiI/AAAAAAAAgFs/u8Z2z76FXdQW_ia55WMHTT0ebeXxXhmUACK8BGAs/s0/2019-07-23.png)"
128+
]
129+
},
130+
{
131+
"cell_type": "code",
132+
"execution_count": 14,
133+
"metadata": {},
134+
"outputs": [
135+
{
136+
"data": {
137+
"text/plain": [
138+
"array([[ 0.6, -0.7],\n",
139+
" [-0.2, 0.4]])"
140+
]
141+
},
142+
"execution_count": 14,
143+
"metadata": {},
144+
"output_type": "execute_result"
145+
}
146+
],
147+
"source": [
148+
"ainv"
149+
]
150+
},
151+
{
152+
"cell_type": "code",
153+
"execution_count": 15,
154+
"metadata": {},
155+
"outputs": [
156+
{
157+
"data": {
158+
"text/plain": [
159+
"array([[1., 0.],\n",
160+
" [0., 1.]])"
161+
]
162+
},
163+
"execution_count": 15,
164+
"metadata": {},
165+
"output_type": "execute_result"
166+
}
167+
],
168+
"source": [
169+
"u = np.eye(2) # unit 2x2 matrix; \"eye\" represents \"I\"\n",
170+
"u"
171+
]
172+
},
173+
{
174+
"cell_type": "code",
175+
"execution_count": 16,
176+
"metadata": {},
177+
"outputs": [
178+
{
179+
"data": {
180+
"text/plain": [
181+
"array([[-1., 0.],\n",
182+
" [ 0., -1.]])"
183+
]
184+
},
185+
"execution_count": 16,
186+
"metadata": {},
187+
"output_type": "execute_result"
188+
}
189+
],
190+
"source": [
191+
"j = np.array([[0.0, -1.0], [1.0, 0.0]])\n",
192+
"j @ j # matrix product"
193+
]
194+
},
195+
{
196+
"cell_type": "code",
197+
"execution_count": 23,
198+
"metadata": {},
199+
"outputs": [
200+
{
201+
"name": "stdout",
202+
"output_type": "stream",
203+
"text": [
204+
"[[3 1]\n",
205+
" [4 5]]\n"
206+
]
207+
},
208+
{
209+
"data": {
210+
"text/plain": [
211+
"8"
212+
]
213+
},
214+
"execution_count": 23,
215+
"metadata": {},
216+
"output_type": "execute_result"
217+
}
218+
],
219+
"source": [
220+
"a = np.array([[3,1],\n",
221+
" [4,5]])\n",
222+
"print(a)\n",
223+
"np.trace(a) # trace"
224+
]
225+
},
226+
{
227+
"cell_type": "code",
228+
"execution_count": 24,
229+
"metadata": {},
230+
"outputs": [
231+
{
232+
"data": {
233+
"text/plain": [
234+
"array([[3, 1],\n",
235+
" [4, 5]])"
236+
]
237+
},
238+
"execution_count": 24,
239+
"metadata": {},
240+
"output_type": "execute_result"
241+
}
242+
],
243+
"source": [
244+
"a"
245+
]
246+
},
247+
{
248+
"cell_type": "code",
249+
"execution_count": 25,
250+
"metadata": {},
251+
"outputs": [
252+
{
253+
"data": {
254+
"text/plain": [
255+
"array([[1.63636364],\n",
256+
" [0.09090909]])"
257+
]
258+
},
259+
"execution_count": 25,
260+
"metadata": {},
261+
"output_type": "execute_result"
262+
}
263+
],
264+
"source": [
265+
"y = np.array([[5.], [7.]])\n",
266+
"np.linalg.solve(a, y)"
267+
]
268+
},
269+
{
270+
"cell_type": "code",
271+
"execution_count": 26,
272+
"metadata": {},
273+
"outputs": [
274+
{
275+
"data": {
276+
"text/plain": [
277+
"array([2., 3.])"
278+
]
279+
},
280+
"execution_count": 26,
281+
"metadata": {},
282+
"output_type": "execute_result"
283+
}
284+
],
285+
"source": [
286+
"a = np.array([[3,1], [1,2]])\n",
287+
"b = np.array([9,8])\n",
288+
"x = np.linalg.solve(a, b)\n",
289+
"x"
290+
]
291+
},
292+
{
293+
"cell_type": "code",
294+
"execution_count": 30,
295+
"metadata": {},
296+
"outputs": [
297+
{
298+
"data": {
299+
"text/plain": [
300+
"True"
301+
]
302+
},
303+
"execution_count": 30,
304+
"metadata": {},
305+
"output_type": "execute_result"
306+
}
307+
],
308+
"source": [
309+
"np.allclose(np.dot(a, x), b)"
310+
]
311+
},
312+
{
313+
"cell_type": "markdown",
314+
"metadata": {},
315+
"source": [
316+
"https://en.wikipedia.org/wiki/Linear_equation\n",
317+
" \n",
318+
"# One Varaiable:\n",
319+
" aX+b= 0\n",
320+
" \n",
321+
" x = -b/a\n",
322+
"\n",
323+
"# Two Variables\n",
324+
" \n",
325+
" ax+bx+c=0\n",
326+
" \n",
327+
" x(a+b)+c=0\n",
328+
" 1/x = -((a+b)+c)\n"
329+
]
330+
}
331+
],
332+
"metadata": {
333+
"kernelspec": {
334+
"display_name": "Python 3",
335+
"language": "python",
336+
"name": "python3"
337+
},
338+
"language_info": {
339+
"codemirror_mode": {
340+
"name": "ipython",
341+
"version": 3
342+
},
343+
"file_extension": ".py",
344+
"mimetype": "text/x-python",
345+
"name": "python",
346+
"nbconvert_exporter": "python",
347+
"pygments_lexer": "ipython3",
348+
"version": "3.6.3"
349+
}
350+
},
351+
"nbformat": 4,
352+
"nbformat_minor": 2
353+
}

0 commit comments

Comments
(0)

AltStyle によって変換されたページ (->オリジナル) /