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Sparse matrices
Sparse Matrices A sparse matrix is a square matrix with zero entries between the diagonal elements. It can be viewed as a matrix where the elements...
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Sparse Matrices A sparse matrix is a square matrix with zero entries between the diagonal elements. It can be viewed as a matrix where the elements...
A sparse matrix is a square matrix with zero entries between the diagonal elements. It can be viewed as a matrix where the elements on the diagonal are non-zero.
Key features:
A sparse matrix has few non-zero elements.
It can be represented using a variety of techniques, such as row-major order or column-major order.
Sparse matrices are often encountered in various data structures and algorithms, such as data mining, machine learning, and signal processing.
Examples:
[1 2 3 0 0 0]
[0 4 5 6 0 0]
[0 0 7 8 9 0]
[0 0 0 10 11 12]
[0 0 0 0 13 14]
[0 0 0 0 15 16]
This is a sparse matrix with only three non-zero elements.
Applications:
Sparse matrices have various applications, including:
Data mining: Sparse matrices can be used for various data mining tasks, such as finding clusters and outliers.
Machine learning: Sparse matrices are used in support vector machines and kernel methods for data analysis.
Signal processing: Sparse matrices are used to represent signals with missing or sparse data.
Image processing: Sparse matrices are used to represent images with missing or important parts.
Additional notes:
The number of non-zero elements in a sparse matrix is called the rank of the matrix.
A sparse matrix with a rank equal to the number of rows is called an upper triangular matrix.
Sparse matrices can be represented using various data structures, such as row vectors or column vectors