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Turn to a linear problem about trace and prove that tr (AB) = tr (BA)
As shown in the picture
What is commutative in matrix multiplication of linear algebra, ab = Ba when commutative
Your new generation?
First of all, we should understand what is matrix multiplication
For example, we know that 3 * 4 = 4 * 3, which means that the multiplication of numbers satisfies the commutative exchange law or "the number pair multiplication in the number field satisfies the commutative exchange law". However, the multiplication of matrices defined in our book generally does not satisfy the commutative exchange law, AB is not necessarily equal to ba
For example, a=
01
00
B=
00
01
In addition, what you call commutativity is actually the abbreviation of "matrix is commutative to multiplication". A * B and matrix AB are on the left and right sides of the multiplication sign. When the commutation position is changed, the result is unchanged, which is commutativity
After you learn the concept of group ring field, you will understand
After the definition of multiplication, for the general group, it is not commutative. The group satisfying commutativity is called "commutative group", "Abel group" or "algebraic plus group"
For example, the addition of a set of matrices of the same order is an Abelian group
When we redefine multiplication on the basis of this addition, we find that the set is an algebraic addition group to addition, a semigroup to multiplication, and the addition satisfies the distributive law to multiplication. Thus a ring is formed
This is a problem discussed in abstract algebra. It is the abstraction of addition, multiplication and division that we see everyday. Since then, not only numbers can do operations, but also sets of matrices and functions can do algebraic operations. Your problem is just to discuss the characteristics of matrix multiplication,
Of course, the multiplication of a matrix does not satisfy the commutative law or the elimination law
If f (x) = x square + 2x-5, then f (x-1) is equal to
Need to do specific process
Just bring it in with X-1
f(x-1)=(x-1)^2+2(x-1)-5
=x^2-2x+1 +2x-2-5
=x^2-6
Fifth grade volume I math oral problems don't answer fast
[training of decimal multiplication and division method] oral test of decimal calculation (1) name () 4 △ 80.054 △ 0.97.5 △ 0.50.8 △ 20.72 △ 1.22.4 △ 0.0335 △ 0.352.2 △ 1.10.18 × 0.58.4 △ 0.060.6 △ 0.150.57 △ 0.191.21 △ 1.10.92 × 0.42.4 × 0.3100 △ 0.25
If the width of a rectangular board is increased by 5 cm, it will become a square and the area will be increased by 75 square cm. What is the original area of this rectangular board
The area is increased by 75 square centimeters because the width is increased by 5 centimeters and the length is unchanged. So the length is s / b = 75 / 5 = 15 centimeters
So the length of the original rectangle is 15 cm, and the width is (15-5) = 10 cm
The original s = a * b = 15 * 10 = 150 square centimeters
How to calculate the instantaneous value of sinusoidal alternating current?
The general formula of alternating current is as follows:
I = im * sin (WT + a), IM is its maximum amplitude, W is the angular frequency, and a is the initial phase
We know:
The effective value is 0.707 * IM, that is, the amplitude divided by the root 2
T=2Pi/w
The amplitude is 14,14 and the angular frequency is 314
The correct answer can be obtained by substituting the corresponding value into the above formula
Divide a square with a circumference of 80cm into four identical rectangles. What are the perimeter and area of each rectangle?
Divide a square with a circumference of 80 cm into four identical rectangles. Each rectangle is 20 long and 5 wide, so it has a circumference of 50 and an area of 100
What is the difference between heart rate, pulse and heartbeat
What are the normal ranges?
Heart rate refers to the number of heart beats per minute, and pulse refers to the number of beats per minute. Heart beat? Heart beat, in non professional terms, is the same as heart rate. Under normal circumstances, heart rate and pulse are the same, but in some cases, they are different. What questions can I ask
It is known that in the cone so, the radius of the bottom surface r = 1, the length of the generatrix L = 4, M is a point on the generatrix SA and SM = X. pull a rope from point m and turn around the side of the cone to point A. (1) find the square of the shortest length of the rope f (x); (2) find the shortest time of the rope, the shortest distance from the fixed point s to the rope; (3) find the maximum value of F (x)
(1) ∵ the radius of the bottom surface r = 1, the length of the generatrix L = 4, and the center angle of the side unfolding sector α = RL × 360 ° = 90 ° therefore, expand the side of the cone into a sector, pull a rope from point m to turn around the side of the cone to point a, the shortest distance is RT △ ASM, the length of the hypotenuse am ∵ SM = x, SA = 4 ∵ f (x) = AM2 = x2 + 42 =
In decimal addition and decimal subtraction, () is the inverse operation of ()
Decimal addition and decimal subtraction (addition) is the inverse operation of (subtraction)!
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