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## Linear algebra

### Course: Linear algebra>Unit 2

Lesson 7: Transpose of a matrix

# Transpose of a matrix

Transpose of a matrix. Created by Sal Khan.

## Want to join the conversation?

• So, you are basically rotating the matrix 90 degrees clockwise, right?
• No, you're mirroring the matrix over the (top-left to bottom-right) diagonal. First row becomes first column and vis-versa, second row becomes second column and vis-versa, nth row becomes nth column and vis-versa.
• Matrixes are very useful in studies where there are lots of data to handle. Matrixes are a useful tool to handle such data. These operations are also used in 3d graphics, games and can also be used in robotic programming.
• how would you use a transpose in every day life
• I used it to write a program for solving a matrix-matrix product, which I then used for various GUI elements. Maybe not "everyday", but certainly useful.
• why is at he just lists mXn why not just list how
• all you do is turn the matrix fraction then you get your answer
• I want to know about conjugate of matrix ??
• Depends what kind of conjugate.
The Hermitian Conjugate (often denoted with a dagger) combines a transpose and a complex conjugate.
For real-valued matrices, the Hermitian conjugate is just the transpose.
• I am writing a paper in math and want to show how one can simply transform digital images using matrices (to represent really broad pixels) (the images are black and white) Is there any way I can use transposition matrices to transform/change my digital images? My matrices represent a portion of the images...I hope this makes any sense! (are there any other cool + simple things I could maybe attempt using matrices?)
• You can change the hue/brightness/orientation etc.

Lets say your colours are stored in a 4x4 matrix, you can change the hue by transforming with this:
{ 1.0, 0.0, 0.0, 0.0,
0.0, 1.0, 0.0, 0.0,
0.0, 0.0, 1.0, 0.0,
roffset, goffset, boffset, 1.0,}
• can i consider the meaning behind a transpose of a particular matrix as a way to find the reflection of that matrix as we can examine whether a matrix is symmetrical or not.
• what does transpose really means? is it changing the rows with the columns in all the cases?

is it changing the