Understanding Matrix Transformations: Question and Solution

Thread starter nokia8650
Start date Jan 29, 2009
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Matrix Transformations

In summary, a matrix transformation is a mathematical operation that uses a matrix to transform coordinates from one system to another. It has a wide range of applications in fields such as computer graphics, physics, engineering, and economics, and can be used for rotations, scaling, shearing, and translations in 3D space. Matrix transformations are represented as 2D arrays or matrices, with each row representing a specific transformation. The main difference between 2D and 3D matrix transformations is the number of rows and columns, allowing 3D matrices to perform more complex transformations. These transformations can affect the size, shape, and orientation of an object, but some, like translations, will preserve its shape.

Jan 29, 2009

nokia8650

Question and solution

http://img141.imageshack.us/img141/4881/74319855am1.th.jpg

http://img141.imageshack.us/img141/1295/58915812pu1.th.jpg

Can someone please explain the solution - why is the right hand matrix
t(k-4)
t(1+k)?

Thanks a lot in advance

Last edited by a moderator: May 3, 2017

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Jan 29, 2009

Werg22

It's the Cayley product of the matrices on the left-hand-side.

FAQ: Understanding Matrix Transformations: Question and Solution

What is a matrix transformation?

A matrix transformation is a mathematical operation that uses a matrix to transform a set of coordinates in a coordinate system to a new set of coordinates.

What are the applications of matrix transformations?

Matrix transformations are used in a wide range of fields, including computer graphics, physics, engineering, and economics. They can be used to rotate, scale, shear, and translate objects in a virtual 3D space, as well as solve systems of linear equations.

How are matrix transformations represented?

Matrix transformations are usually represented in the form of a 2D array or matrix, with the transformation operation applied to a set of coordinates represented as a column vector. Each row of the matrix represents the transformation applied to a specific coordinate.

What is the difference between a 2D and 3D matrix transformation?

A 2D matrix transformation operates on points in a 2D space, while a 3D matrix transformation operates on points in a 3D space. This means that a 3D matrix has an additional row and column compared to a 2D matrix, and can perform more complex transformations such as rotating objects in 3D space.

How do matrix transformations affect the shape of an object?

Matrix transformations can modify the size, shape, and orientation of an object. For example, a scaling matrix will increase or decrease the size of an object, while a rotation matrix will change its orientation. Some transformations may also preserve the shape of an object, such as translations, which only change its position in space.