Definition:Rank/Linear Transformation

Definition

Let $\phi$ be a linear transformation from one vector space to another.

Let the image of $\phi$ be finite-dimensional.

Then its dimension is called the rank of $\phi$ and is denoted $\map \rho \phi$.

Also see

• Results about rank of linear transformation can be found here.

Sources

• 1965: Seth Warner: Modern Algebra ... (previous) ... (next): Chapter $\text {V}$: Vector Spaces: $\S 28$. Linear Transformations
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): rank: 3. (of a matrix)
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): rank: 3. (of a matrix)

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