NumPy Matrix Operations and Linear Algebra Exercises

Last update on March 25 2025 12:17:40 (UTC/GMT +8 hours)

This resource offers a total of 95 NumPy Linear Algebra problems for practice. It includes 19 main exercises, each accompanied by solutions, detailed explanations, and four related problems.

This document showcases advanced linear algebra operations using NumPy, including various matrix products, decompositions, and computations of determinants, eigenvalues, and norms.

[An Editor is available at the bottom of the page to write and execute the scripts.]

1. Matrix Multiplication

Write a NumPy program to compute the multiplication of two given matrixes.

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2. Outer Product of Vectors

Write a NumPy program to compute the outer product of two given vectors.

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3. Cross Product of Vectors

Write a NumPy program to compute the cross product of two given vectors.

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4. Determinant of a Square Array

Write a NumPy program to compute the determinant of a given square array.

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5. Einstein Summation Convention

Write a NumPy program to evaluate Einstein's summation convention of two given multidimensional arrays.

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6. Inner Product of Vectors

Write a NumPy program to compute the inner product of vectors for 1-D arrays (without complex conjugation) and in higher dimension.

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7. Eigenvalues and Eigenvectors

Write a NumPy program to compute the eigenvalues and right eigenvectors of a given square array.

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8. Kronecker Product

Write a NumPy program to compute the Kronecker product of two given mulitdimension arrays.

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9. Condition Number of a Matrix

Write a NumPy program to compute the condition number of a given matrix.

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10. Matrix or Vector Norm

Write a NumPy program to find a matrix or vector norm.

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11. Determinant of an Array

Write a NumPy program to compute the determinant of an array.

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12. Inverse of a Matrix

Write a NumPy program to compute the inverse of a given matrix.

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13. QR Decomposition

Write a NumPy program to calculate the QR decomposition of a given matrix.

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14. Condition Number (Alternate)

Write a NumPy program to compute the condition number of a given matrix.

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15. Sum of Diagonal Elements

Write a NumPy program to compute the sum of the diagonal element of a given array.

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16. Cholesky Decomposition (Lower-Triangular Factor)

Write a NumPy program to get the lower-triangular L in the Cholesky decomposition of a given array.

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17. QR Factorization

Write a NumPy program to get the qr factorization of a given array.

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18. Singular Value Decomposition (SVD)

Write a NumPy program to compute the factor of a given array by Singular Value Decomposition.

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19. Frobenius Norm and Condition Number

Write a NumPy program to calculate the Frobenius norm and the condition number of a given array.

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