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  • Givens rotation
  • {2}c_{1}+s_{3}s_{1}&c_{3}s_{2}s_{1}+s_{3}c_{1}&c_{3}c_{2}\end{bmatrix}}} zxz [ c 3 c 1 − c 2 s 1 s 3 − c 3 s 1 − c 1 c 2 s 3 s 2 s 3 c 2 c 3 s 1 + c 1

  • Euler angles
  • Here we present the results for the two most commonly used conventions: ZXZ for proper Euler angles and ZYX for Tait–Bryan. Notice that any other convention

  • Group action
  • R3: for any such quaternion z = cos α/2 + v sin α/2, the mapping f(x) = zxz* is a counterclockwise rotation through an angle α about an axis given by

  • Inverse element
  • has at least one inverse: if x = xzx then it is easy to verify that y = zxz is an inverse of x as defined in this section. Another easy to prove fact:

  • Spherical 3-manifold
  • x y , z 3 k = 1 ⟩ {\displaystyle \langle x,y,z\mid (xy)^{2}=x^{2}=y^{2},zxz^{-1}=y,zyz^{-1}=xy,z^{3^{k}}=1\rangle } for integers k, m with k ≥ 1, m ≥

  • Moufang loop
  • example, the Moufang identities may be written unambiguously as z(x(zy)) = (zxz)y ((xz)y)z = x(zyz) (zx)(yz) = z(xy)z. The Moufang identities can be written

  • Band (algebra)
  • any semigroup the first identity also implies the second because xyz = xy(zxz) = (x(yz)x)z = xz. The idempotents of a rectangular semigroup form a sub

  • Bergman's diamond lemma
  • z x z = x z 2 = x ( x y + y x ) = x 2 y + x y x . {\displaystyle z^{2}x=zxz=xz^{2}=x(xy+yx)=x^{2}y+xyx.} Since both of the above are reduced but not

  • Granny knot (mathematics)
  • = y x y , x z x = z x z ⟩ . {\displaystyle \langle x,y,z\mid xyx=yxy,xzx=zxz\rangle .} This is isomorphic to the knot group of the square knot, and is

  • Conjugacy problem
  • there exists an element z of G such that y = z x z − 1 . {\displaystyle y=zxz^{-1}.\,\!} The conjugacy problem is also known as the transformation problem

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Astrological/horoscope meaning of zxzly. zxzly means: With a Life Path 5, your numbers are (5, 14/5, 23/5, 32/5). Life path 5 shows that you entered life with a progressive attitude, with the attitude and the skills to make the world a better place. The key word in your life path is freedom. In the pursuit of freedom, you are naturally versatile, adventurous, and advanced in your thinking. You are one of those people who are always trying to find answers to the many questions that life presents. 5 for positive life path is change and continuous improvement. You want to be completely unrestrained, as the number most associated with the productive use of freedom.You are one of the most compassionate people. A life path of 5 means you appreciate with certainty the way a freedom-loving and a compassionate life. Your love of freedom extends to humanity in general, and concern for one's neighbor, the freedom and well-being, perhaps especially in the mind. A great path life of 5 is US President Abraham Lincoln who declared slave Emancipation Proclamation, and ended slavery in America. As the ultimate progressive thinkers your potential in the Government give you considerable knowledge to exercise authority on others.You are a good communicator, and you know how to motivate people around you. This can be your feature that is the strongest and be the most valuable. Because of this ability, and your amazing mind, you are a really born leader able to sell his views. This ability to sell and motivate extends to any kind of physical product in all ideas or concepts that you can undertake.They hate routine work because it gets boring, and you are not very good to stay with the daily tasks that must be completed in bitcoin?. On average, the number 5 personality live for today, and not too much about tomorrow. It is also important that you find a job that provides challenging tasks rather than routine and redundant tasks. They deal better with people, but the important thing is he person. With the ability to express yourself anytime, you have an innate ability to think through complex issues and to analyze it quickly even when it is something new.An adventure can dominate your life. This can take the form of physical or mental manifestation, but in both cases you will have the chance for exploration thrills and new ways. Of course, you belong to a group considered most secular and traveled. Obviously you do not ignore a good adventure. You take lot of risk, but often come out successful. If you do not have your own money at stake, you are even more open for a wide range of risks in your daily life. the conservative approach is simply not found in your nature.In romance, you dislike the limits imposed by love. You would like to be boundless. This does not necessarily mean you are unfaithful or promiscuous, but that does not mean you also make a good partner, you need to understand your style. A relationship that is governed on jealousy and narrow-mindedness will not work for you. You need a partner who understands your needs, is trustworthy, can see your trustworthiness, even if you are not always available and to be fully devoted. It is important that you mix with people who are different, and try those who are too serious and avoid demanding tasks.If you live on the negative side of life path 5, you are likely to be versatile, but suffer from a lack of direction, and there is confusion surrounding your ambition. Restless, discontent, and impulsive, you can choose to jump from one job to another without ever finding satisfaction with any. 5 in a negative way of life can be very irresponsible in tasks and decisions about the life of the home and business. The total pursuit of sensation and adventure in you may make you to completely ignore the feelings of those around you.

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    Z: Meaning of Z in the acronym zxzly means: The letter Z zigzags forward and backwards to explore both the left and right sides of the universe. It's bottom is flat showing a certain degree of stability. Z is determined and helpful. The lower and upper cases of Z look the same indicating Z is unchanging, highly esteemed, immense and compelling.

    X: Meaning of X in the acronym zxzly means: X is a cross bettween two arms of exactly the same lenght. It also balances on two ends at the bottom. It looks like Y with the bottom ends merged in the middle. X is stable, responsible, gorgeous, and spiritual as it opens upwards. X also shows enlightenment as it seeks to explore by extending its arms.

    L: Meaning of L in the acronym zxzly means: The letter has a flat bottom and a vertically extending part that projects into the sky. L is aspiring, reckoning, methodical, logical and convincing. Its flat bottom on the earth shows desire for earthly things hence L is materialistics and active. L is flexible, successful, public, insightful and considerate.

    Y: Meaning of Y in the acronym zxzly means: Y is a mystic character. It lies on one leg spreading two arms out upwards and outwards. Y seems to be yearning for something from above. It is mystic, reserved, affecting yet self-governing. The separate arms shows why is separate and it could also be troublesome if it receives mystical powers.

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