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Symbols · Operators and calculus

ᵀ Transpose

Say it: “transpose”

What it means

A superscript T flips a matrix over its diagonal, so rows become columns. A column vector transposed is a row vector, which is how dot products are written as matrix products.

Read aloud in real formulas

Linear algebra

(AB)ᵀ = BᵀAᵀ

Aethel says

the quantity A B, transpose equals B transpose A transpose

transposing a product reverses the order

Machine learning

softmax(QKᵀ / √dₖ)

Aethel says

softmax of the quantity QK transpose over the square root of d sub k

every query against every key

Typing it

LaTeX
A^\top, A^T
Unicode
U+1D40

Formulas that use it

Questions

How do you say ᵀ out loud?

It is usually read “transpose”.

What does ᵀ mean in maths?

A superscript T flips a matrix over its diagonal, so rows become columns. A column vector transposed is a row vector, which is how dot products are written as matrix products.

How do you type ᵀ?

In LaTeX, write A^\top, A^T. Its Unicode code point is U+1D40.

Related symbols

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