mldivide, \

R2026b

Quaternion left division for scalars

Syntax

C = A\B

Description

C = A\B performs left division between a scalar and a quaternion or array of quaternions.

Examples

Left Divide Quaternion Array by Real Scalar

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

A = quaternion([1:4;5:8])

A = 2×1 quaternion array
     1 + 2i + 3j + 4k
     5 + 6i + 7j + 8k

B = 2;
C = A\B

C = 2×1 quaternion array
     0.066667 -  0.13333i -      0.2j -  0.26667k
     0.057471 - 0.068966i -  0.08046j - 0.091954k

Left Divide Quaternion Array by Quaternion Scalar

Create a 2-by-2 quaternion array, and left divide it by a quaternion scalar.

q1 = quaternion(magic(4));
A = reshape(q1,2,2)

A = 2×2 quaternion array
     16 +  2i +  3j + 13k      9 +  7i +  6j + 12k
      5 + 11i + 10j +  8k      4 + 14i + 15j +  1k

B = quaternion([1:4])

B = quaternion
     1 + 2i + 3j + 4k

C = A\B

C = 2×2 quaternion array
       0.18493 +   0.13014i +  0.061644j +   0.11644k        0.2871 +  0.074194i +  0.080645j +  0.048387k
        0.2871 -  0.054839i +   0.10645j - 0.0032258k       0.18493 -   0.14384i +   0.11644j + 0.0068493k

Input Arguments

A — Divisor

quaternion object | array of quaternion objects | real scalar | array of real numbers

Divisor, specified as a quaternion object, an array of quaternion objects, a real numeric scalar, or an array of real numbers. Numeric values must be of data type single or double.

At least one of A and B must a scalar.

B — Dividend

quaternion object | array of quaternion objects | real scalar | array of real numbers

Dividend, specified as a quaternion object, an array of quaternion objects, a real numeric scalar, or an array of real numbers. Numeric values must be of data type single or double.

At least one of A and B must a scalar.

Output Arguments

C — Result

quaternion object | array of quaternion objects

Result of quaternion left division, returned as a quaternion object or an array of quaternion objects.

Algorithms

Quaternion Division

Given a quaternion $$A=a_1+a_2\text{i}+a_3\text{j}+a_4\text{k}$$ and a real numeric scalar p,

$$C=p\backslash A=\frac{a_1}{p}+\frac{a_2}{p}\text{i}+\frac{a_3}{p}\text{j}+\frac{a_4}{p}\text{k}$$

Note

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

Quaternion Division by a Quaternion Scalar

Given two quaternions A and B,

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

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

GPU Code Generation
Generate CUDA® code for NVIDIA® GPUs using GPU Coder™.