Examples of 'quaternion' in a sentence
Meaning of "quaternion"
quaternion (noun) - a mathematical concept that extends the complex numbers into four dimensions
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- A group or set of four people or things.
- A word of four syllables.
- A type of four-dimensional hypercomplex number consisting of a real part and three imaginary parts (real multiples of distinct, independent square roots of −1 denoted by i, j and k); commonly used in vector mathematics and as an alternative to matrix algebra in calculating the rotation of three-dimensional objects.
How to use "quaternion" in a sentence
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quaternion
Note that quaternion multiplication is not commutative.
Such a set of four numbers is called a quaternion.
A unit quaternion can be used to represent rotations.
We can convert the rotation matrix to a quaternion.
The quaternion associated with the rotation is.
The rotation is calculated using quaternion as follows.
A unit quaternion is a quaternion of norm one.
In computational implementations this requires two quaternion multiplications.
The quaternion form a division algebra.
Converting a rotation to quaternion is straightforward.
A quaternion is then a number of the form.
Thus we have the quaternion.
Hamilton defined a quaternion as the quotient of two vectors.
Quaternion is an inexhaustible source of life.
The product of two quaternions is called quaternion product.
See also
Fueter did research on algebraic number theory and quaternion analysis.
A quaternion can be represented as the sum of a scalar and a vector.
It is represented internally as a unit quaternion.
Classical quaternion notation had only one concept of multiplication.
The orientation of the pen may also be represented by quaternion.
Each real quaternion is carried into itself by this operation.
Fast rotation of a vector by a quaternion.
A quaternion consists of a scalar part and a complex vector part.
The real component of a quaternion is also called its scalar part.
Quaternion multiplication is associative.
A vector plus a scalar is always a quaternion even if the scalar is zero.
The quaternion numbers.
Thus q a is a real quaternion.
The conjugate of a quaternion corresponds to the conjugate transpose of the matrix.
Hurwitz integral quaternion.
The product of a quaternion with its conjugate is its common norm.
All rotation differential values are represented by unit quaternion expression values.
The vector part of a quaternion is also called the right part.
It could also be a quaternion.
It is preferable to use the quaternion symbolism that yields quadratic functions.
Quaternion is a poetry style in which the theme is divided into four parts.
Generalised quaternion group.
Sometimes a redundant fourth number is added to simplify operations with quaternion algebra.
Generalized quaternion group.
The position of said space station is also obtained on the basis of a quaternion calculation.
Each part of a quaternion explores the complementary natures of the theme or subject.
We also dealt with obtaining a quaternary root of a quaternion and a real number.
The square of a quaternion rotation is a rotation by twice the angle around the same axis.
Note on a quaternion.
The generalized quaternion groups have the property that every abelian subgroup is cyclic.
This is a quaternion.
The quaternion so obtained will correspond to the rotation matrix closest to the given matrix.
The fourth power of the norm of a quaternion is the determinant of the corresponding matrix.
This representation differs slightly from a more common representation found in the quaternion article.
Error compensation and filtering are performed with quaternion notation to provide computational efficiency.
