# Transpose of a matrix | Matrix transformations | Linear Algebra | Khan Academy | Summary and Q&A

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November 4, 2009
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Transpose of a matrix | Matrix transformations | Linear Algebra | Khan Academy

## TL;DR

Matrix transpose involves swapping the rows and columns of a matrix, resulting in a new matrix with the dimensions flipped.

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### Q: What is matrix transpose?

Matrix transpose is the operation of swapping the rows and columns of a matrix, resulting in a new matrix with the dimensions flipped.

### Q: How is matrix transpose denoted?

The transpose of a matrix A is typically denoted as A^T or A with superscript T.

### Q: Do all matrices have a transpose?

Yes, all matrices can have a transpose, although the dimensions of the resulting transposed matrix will be different from the original.

### Q: What is the relationship between matrix transpose and matrix dimensions?

The transpose of an m x n matrix will result in an n x m matrix. The number of rows in the original matrix becomes the number of columns in the transposed matrix, and vice versa.

## Summary & Key Takeaways

• Matrix transpose involves swapping the rows and columns of a matrix.

• The transpose of an m x n matrix results in an n x m matrix.

• The entries of the original matrix become columns in the transposed matrix.