Home > manopt > manifolds > essential > essential_hat3.m

# essential_hat3

## PURPOSE

Compute the matrix representation of the cross product

## SYNOPSIS

function [V, vShift] = essential_hat3(v)

## DESCRIPTION

```Compute the matrix representation of the cross product
function [V,vShift] = essential_hat3(v)
V is a [3x3xN] array of skew-symmetric matrices where each [3x3] block is
the matrix representation of the cross product of one of the columns of v
vShift is equal to permute(v,[1 3 2]).```

## CROSS-REFERENCE INFORMATION

This function calls:
This function is called by:
• essential_svd Sample solution of an optimization problem on the essential manifold.
• essentialfactory Manifold structure to optimize over the space of essential matrices.

## SOURCE CODE

```0001 %Compute the matrix representation of the cross product
0002 %function [V,vShift] = essential_hat3(v)
0003 %V is a [3x3xN] array of skew-symmetric matrices where each [3x3] block is
0004 %the matrix representation of the cross product of one of the columns of v
0005 %vShift is equal to permute(v,[1 3 2]).
0006 function [V, vShift] = essential_hat3(v)
0007     N = size(v,2);
0008     V = zeros(3,3,N);
0009     vShift = permute(v,[1 3 2]);
0010     V(1,2,:) = -vShift(3,:,:);
0011     V(2,1,:) = vShift(3,:,:);
0012     V(1,3,:) = vShift(2,:,:);
0013     V(3,1,:) = -vShift(2,:,:);
0014     V(2,3,:) = -vShift(1,:,:);
0015     V(3,2,:) = vShift(1,:,:);
0016 end```

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