Online Matrix Rank Analyzer
Compute matrix rank, RREF, and visualize basis vectors for your matrix.
Matrix Input
Results
RREF, rank, pivot columns, and basis sets
Notes
Visualization supports up to 3 dimensions. For higher dimensions, basis vectors are shown as text.
How To Use
Step-by-step guide to using the Matrix Rank Analyzer
Enter Matrix
Input your matrix in the text area
Choose Example
Use preset examples or enter your own
Analyze Matrix
Click Analyze to compute rank and basis
Explore Results
View RREF, rank, and basis vectors
Matrix rank is a fundamental concept in linear algebra that measures the dimension of the vector space spanned by the matrix columns. It represents the maximum number of linearly independent rows or columns in the matrix.
The rank-nullity theorem connects matrix rank with the dimension of the null space, providing crucial insights into the solution space of linear systems. Understanding matrix rank helps in determining system consistency and analyzing linear transformations.
Applications of Matrix Rank:
- Linear Systems: Determining solution existence and uniqueness
- Linear Independence: Checking vector independence in vector spaces
- Image Processing: Analyzing image transformations and compressions
- Data Analysis: Principal component analysis and dimensionality reduction
- Cryptography: Basis for encryption algorithms and error-correcting codes
- Graph Theory: Analyzing adjacency matrix properties and connectivity
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