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NumPy Linear Algebra: Exercises, Practice, Solution

NumPy Linear Algebra [19 exercises with solution]

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Linear algebra: Pictorial Presentation

1. Write a NumPy program to compute the multiplication of two given matrixes. Go to the editor
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2. Write a NumPy program to compute the outer product of two given vectors. Go to the editor
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3. Write a NumPy program to compute the cross product of two given vectors. Go to the editor
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4. Write a NumPy program to compute the determinant of a given square array. Go to the editor
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5. Write a NumPy program to evaluate Einstein's summation convention of two given multidimensional arrays. Go to the editor
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6. Write a NumPy program to compute the inner product of vectors for 1-D arrays (without complex conjugation) and in higher dimension. Go to the editor
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7. Write a NumPy program to compute the eigenvalues and right eigenvectors of a given square array. Go to the editor
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8. Write a NumPy program to compute the Kronecker product of two given mulitdimension arrays. Go to the editor
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9. Write a NumPy program to compute the condition number of a given matrix. Go to the editor
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10. Write a NumPy program to find a matrix or vector norm. Go to the editor
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11. Write a NumPy program to compute the determinant of an array. Go to the editor
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12. Write a NumPy program to compute the inverse of a given matrix. Go to the editor
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13. Write a NumPy program to calculate the QR decomposition of a given matrix. Go to the editor
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14. Write a NumPy program to compute the condition number of a given matrix. Go to the editor
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15. Write a NumPy program to compute the sum of the diagonal element of a given array. Go to the editor
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16. Write a NumPy program to get the lower-triangular L in the Cholesky decomposition of a given array. Go to the editor
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17. Write a NumPy program to get the qr factorization of a given array. Go to the editor
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18. Write a NumPy program to compute the factor of a given array by Singular Value Decomposition. Go to the editor
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19. Write a NumPy program to calculate the Frobenius norm and the condition number of a given array. Go to the editor
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Python: Tips of the Day

Find the index of an item in a list?

Given a list ["foo", "bar", "baz"] and an item in the list "bar", how do I get its index (1) in Python?

>>> ["foo", "bar", "baz"].index("bar")
1

Caveats follow

Note that while this is perhaps the cleanest way to answer the question as asked, index is a rather weak component of the list API, and I can't remember the last time I used it in anger. It's been pointed out to me in the comments that because this answer is heavily referenced, it should be made more complete. Some caveats about list.index follow. It is probably worth initially taking a look at the documentation for it:

list.index(x[, start[, end]])

Linear time-complexity in list length

An index call checks every element of the list in order, until it finds a match. If your list is long, and you don't know roughly where in the list it occurs, this search could become a bottleneck. In that case, you should consider a different data structure. Note that if you know roughly where to find the match, you can give index a hint. For instance, in this snippet, l.index(999_999, 999_990, 1_000_000) is roughly five orders of magnitude faster than straight l.index(999_999), because the former only has to search 10 entries, while the latter searches a million:

>>> import timeit
>>> timeit.timeit('l.index(999_999)', setup='l = list(range(0, 1_000_000))', number=1000)
9.356267921015387
>>> timeit.timeit('l.index(999_999, 999_990, 1_000_000)', setup='l = list(range(0, 1_000_000))', number=1000)
0.0004404920036904514

Only returns the index of the first match to its argument

A call to index searches through the list in order until it finds a match, and stops there. If you expect to need indices of more matches, you should use a list comprehension, or generator expression.

>>> [1, 1].index(1)
0
>>> [i for i, e in enumerate([1, 2, 1]) if e == 1]
[0, 2]
>>> g = (i for i, e in enumerate([1, 2, 1]) if e == 1)
>>> next(g)
0
>>> next(g)
2

Most places where I once would have used index, I now use a list comprehension or generator expression because they're more generalizable. So if you're considering reaching for index, take a look at these excellent Python features.

Throws if element not present in list

A call to index results in a ValueError if the item's not present.

>>> [1, 1].index(2)
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
ValueError: 2 is not in list

If the item might not be present in the list, you should either

  • Check for it first with item in my_list (clean, readable approach), or
  • Wrap the index call in a try/except block which catches ValueError (probably faster, at least when the list to search is long, and the item is usually present.)

Ref: https://bit.ly/2ALwXwe