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Linear Algebra

Rank

The rank of a matrix is the dimension of its row space or column space and measures the number of independent directions.

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Meaning

What Is Rank?

The rank of a matrix is the dimension of its row space or column space and measures the number of independent directions.

The rank of a matrix is the dimension of its row space or column space and measures the number of independent directions.

Examples

Examples of Rank

1A matrix with one non-zero independent row has rank 1.
Understand

Formula and Key Points

Formula / rule
rank(A)
  • Know the definition and standard notation for Rank.
  • Be able to recognise or compute rank in a small example.
  • Connect the concept to nearby topics in the same subject before using it in larger CSE problems.
CSE Connection

Why This Matters in Computer Science

Used in computer graphics, machine learning, computer vision, signal processing, robotics and scientific computing.

FAQ

Rank: Frequently Asked Questions

What is Rank?

The rank of a matrix is the dimension of its row space or column space and measures the number of independent directions.

Why is Rank useful in computer science?

Used in computer graphics, machine learning, computer vision, signal processing, robotics and scientific computing.