Projection Matrices and Subspaces

To project vectors onto a subspace

To rotate vectors in space

To reflect vectors across a plane

To scale vectors uniformly

X - Y - Z = 0

X + Y - Z = 0

X - Y + Z = 0

X + Y + Z = 0

It defines the normal vector to the plane

It encodes the subspace being projected onto

It represents the identity matrix

It is used to scale the projection

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It reflects the normal vector

It scales the normal vector by half

It projects the normal vector to zero

It doubles the normal vector

Using a different basis for the plane

Applying a rotation matrix

Projecting onto the normal vector first

Using the inverse of the identity matrix

It requires fewer calculations

It uses a larger determinant

It is less accurate

It involves more complex matrices

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Add the identity matrix

Subtract from the identity matrix

Divide by the determinant

Multiply by the normal vector