ldivide, .\

Element-wise quaternion left division

Description

example

C = A.\B performs quaternion element-wise division by dividing each element of quaternion B by the corresponding element of quaternion A.

Examples

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Create a 2-by-1 quaternion array, and divide it element-by-element by a real scalar.

A = quaternion([1:4;5:8])
A = 2x1 quaternion array
1 + 2i + 3j + 4k
5 + 6i + 7j + 8k

B = 2;
C = A.\B
C = 2x1 quaternion array
0.066667 -  0.13333i -      0.2j -  0.26667k
0.057471 - 0.068966i -  0.08046j - 0.091954k

Create a 2-by-2 quaternion array, and divide it element-by-element by another 2-by-2 quaternion array.

q1 = quaternion([1:4;2:5;4:7;5:8]);
A = reshape(q1,2,2)
A = 2x2 quaternion array
1 + 2i + 3j + 4k     4 + 5i + 6j + 7k
2 + 3i + 4j + 5k     5 + 6i + 7j + 8k

q2 = quaternion(magic(4));
B = reshape(q2,2,2)
B = 2x2 quaternion array
16 +  2i +  3j + 13k      9 +  7i +  6j + 12k
5 + 11i + 10j +  8k      4 + 14i + 15j +  1k

C = A.\B
C = 2x2 quaternion array
2.7 -      1.9i -      0.9j -      1.7k       1.5159 -  0.37302i -  0.15079j -  0.02381k
2.2778 +  0.46296i -  0.57407j + 0.092593k       1.2471 +  0.91379i -  0.33908j -   0.1092k

Input Arguments

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Divisor, specified as a quaternion, an array of quaternions, a real scalar, or an array of real numbers.

A and B must have compatible sizes. In the simplest cases, they can be the same size or one can be a scalar. Two inputs have compatible sizes if, for every dimension, the dimension sizes of the inputs are the same or one of the dimensions is 1.

Data Types: quaternion | single | double

Dividend, specified as a quaternion, an array of quaternions, a real scalar, or an array of real numbers.

A and B must have compatible sizes. In the simplest cases, they can be the same size or one can be a scalar. Two inputs have compatible sizes if, for every dimension, the dimension sizes of the inputs are the same or one of the dimensions is 1.

Data Types: quaternion | single | double

Output Arguments

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Result of quaternion division, returned as a scalar, vector, matrix, or multidimensional array.

Data Types: quaternion

Algorithms

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Quaternion Division

Given a quaternion $A={a}_{1}+{a}_{2}\text{i}+{a}_{3}\text{j}+{a}_{4}\text{k}$ and a real scalar p,

$C=p.\A=\frac{{a}_{1}}{p}+\frac{{a}_{2}}{p}\text{i}+\frac{{a}_{3}}{p}\text{j}+\frac{{a}_{4}}{p}\text{k}$

Note

For a real scalar p, A./p = A.\p.

Quaternion Division by a Quaternion Scalar

Given two quaternions A and B of compatible sizes, then

$C=A.\B={A}^{-1}.*B=\left(\frac{conj\left(A\right)}{norm{\left(A\right)}^{2}}\right).*B$