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How to find the modular formula of matrix
Which module? Although the modules of a finite dimensional space are equivalent, some of them are very easy to calculate (for example, adding the absolute values of all elements of a matrix), and some of them are very troublesome (for example, finding the L2 module)
Matrix formula for mathematical problems
Matrix multiplication formula:
For example:
1 2 1 2 3 4
A = 2 5 3 B = 1 5 2
1 3 4 3 6 7
A * B =
Detailed calculation process
.1*2+2*1+1*3..1*3+2*5+1*6..1*4+2*2+1*7..7.19.15
A*B=2*2+5*1+3*3..2*3+5*5+3*6..2*4+5*2+3*7=18.49.39
.1*2+3*1+4*3..1*3+3*5+4*6..1*4+3*2+4*7..17.42.38
... denotes a space
The rule is to multiply the i-th row of the preceding matrix and the j-th column of the following matrix and add them to the (I, J) position of the resulting matrix
What is the covariance matrix formula?
In statistics and probability theory, covariance matrix (or covariance matrix) is a matrix, each element of which is the variance between each vector element. This is a natural generalization from scalar random variables to high-dimensional random vectors. Suppose x is a column vector composed of N scalar random variables, and μ I & nbsp; is its th
Interesting thing composition 400 words
Childhood, some people say, is a small box filled with all kinds of interesting things, some people say it is a dream of happiness and laughter, so let's go to open the shackles of childhood and recall our happy childhood. In the summer when I was five years old, the sky was hot and the asphalt road could roast mutton kebabs
Three consecutive integers, the sum of the squares of the first two integers is equal to the square of the third number. Can you find out the respective numbers of these three integers?
Let the middle integer be x, then the first one is X-1, and the third one is x + 1. According to the meaning of the question, we get (x-1) 2 + x2 = (x + 1) 2, and the solution is X1 = 4, X2 = 0, then X-1 = 3, x + 1 = 5, or X-1 = - 1, x + 1 = 1, x = 0. Answer: these three integers are 3, 4, 5 or - 1, 0, 1
350 gas shielded welding machine can weld 0.8 thick iron plate? How to adjust the current? I often weld 0.8-8 mm
A: 350 gas shielded welding with good performance can weld 0.8 steel plate
The parameters are as follows:
Butt welding: current 60 ~ 70A, voltage 17 ~ 18V
Welding: current 80 ~ 100A, voltage 18 ~ 20V
Of course, the welding wire is 0.8, so the welding speed should be faster!
What are the strange scenes in nature
Every scene in nature is a miracle, but you don't pay attention to details. What you call strange is only a few scenes on the earth. For example, a tree has lived for two thousand years, and there is only one tree on the whole earth. Compared with other life, the age of this tree is strange. But our telescope can see hundreds of millions of stars in space, It's not strange that there is only life on the earth
A simple method is used to calculate the known value of x = (5 + 1 under the root) divided by 2, and find the value of the third power of X divided by (cube of X + X + 1)
x²=(√5＋3)／2, x³=√5＋2
1／x²=0.5(3-√5) 1／x³=（√5-2）
x³／（x³＋x＋1）=1／（1＋1／x²＋1／x³）==(√5-1)／2
Let a and B be any two nonzero matrices satisfying AB = 0, then there must be linear correlation between the column vectors of (a) a and the row vectors of B
Let a and B be any two nonzero matrices satisfying AB = 0
(A) The column vector group of a is linearly correlated, and the row vector group of B is linearly correlated
(B) The column vector group of a is linear correlation, and the column vector group of B is linear correlation
(C) The row vector group of a is linear correlation, and the row vector group of B is linear correlation
(D) The row vector group of a is linearly correlated, and the column vector group of B is linearly correlated
My question is: why is d wrong?
The steps in the book are:
Let a be mxn matrix, B be NXS matrix, satisfy AB = 0, and both a and B are nonzero matrices, then
R (a) + R (b) ≤ n, R (a) ≥ 1, R (b) ≥ 1, so there must be r (a) < n and R (b) < n
Therefore, the column vector group of a is linearly correlated, and the row vector group of B is linearly correlated. A
Here's a counterexample
A=
1 0 1 2
0 1 3 4
B=
1 2
3 4
-1 0
0 -1
In △ ABC, ab = AC, ∠ BAC = 80 °, P in △ ABC, ∠ PBC = 10 °, PCB = 20 °, then the degree of ∠ PAB is ()
A. 50°B. 60°C. 70°D. 65°
As shown in the figure, make the symmetry point P 'of P with respect to AC, connect AP', p 'C and PP', then p 'C = PC, ACP' = ∠ ACP. ∵ AB = AC, ∵ BAC = 80 °, and ∵ ABC = ∵ ACB = 50 °, and ∵ PBC = 10 °, PCB = 20 °, BPC = 150 °, ACP = 30 °, ACP '= 30 °, PCP' = 60 ° and ∵ PCP 'are equilateral triangles, ∵ PP' = PC, ∵ p 'AC = ∵ PAC, ∵ p' PC = 60 °, BPP '= 360 ° - 150 ° - 60 ° = 150 °, ∠ BPP ′ = ∠ BPC, △ PBP ′ ≌ △ PBC, PBP ′ = ∠ PBC = 10 °, ∠ P ′ BC = 20 ° and ∠ ABP ′ = 30 ° and ∠ ACP ′ = 30 °, the four points a, B, C and P ′ are in common circle, and ∠ PAC = ∠ P ′ AC = ∠ P ′ BC = 20 ° and ∠ PAB = 60 °. Therefore, B is selected
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