📅 Day 58 of My Data Analytics Journey

Today I dived into Linear Algebra concepts in NumPy 🤓
These operations are essential in Machine Learning, Data Science, and Deep Learning because they help us work with vectors, matrices, and transformations used in models like *Neural *

Here’s what I learned 👇

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✅ 1️⃣ Dot Product (np.dot())

📌 What it does

Multiplies two vectors/matrices. Used in ML for calculating weights × features.

🧠 Example

import numpy as np

a = np.array([1, 2])
b = np.array([3, 4])

result = np.dot(a, b)
print(result)  # Output: 11

Calculation → (1*3 + 2*4) = 11

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✅ 2️⃣ Inner Product (np.inner())

📌 What it does

Same as dot product for 1D vectors, but behaves differently for higher dimensions.

🧠 Example

a = np.array([1, 2])
b = np.array([3, 4])

print(np.inner(a, b))  # Output: 11

For simple vectors, inner = dot

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✅ 3️⃣ Outer Product (np.outer())

📌 What it does

Creates a matrix by multiplying each element of a vector with another.

🧠 Example

print(np.outer(a, b))

Output

[[3 4]
 [6 8]]

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✅ 4️⃣ Determinant (np.linalg.det())

📌 What it does

Determines if a matrix is invertible (used in solving linear equations)

🧠 Example

m = np.array([[2, 3], 
              [1, 4]])

print(np.linalg.det(m))  # Output: 5.0

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✅ 5️⃣ Solve Linear Equations (np.linalg.solve())

📌 Example: Solve Ax = B

A = np.array([[2, 1],
              [1, 3]])

B = np.array([8, 13])
x = np.linalg.solve(A, B)

print(x)  # Output: [3. 5.]

Solution → x = 3, y = 5

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✅ 6️⃣ Inverse of Matrix (np.linalg.inv())

📌 What it does

Computes matrix inverse (important in ML algorithms like normal equation)

print(np.linalg.inv(m))

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✅ 7️⃣ Trace (np.trace())

📌 What it does

Sum of diagonal elements

print(np.trace(m))  # Output: 6

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🎯 Summary Table

Operation	Meaning	NumPy
Dot Product	Feature-weight multiplication	np.dot()
Inner Product	Similar to dot (1D)	np.inner()
Outer Product	Builds matrix from vectors	np.outer()
Determinant	Matrix validity	np.linalg.det()
Solve	Solve Ax = B	np.linalg.solve()
Inverse	Reverse matrix effect	np.linalg.inv()
Trace	Sum of diagonal values	np.trace()

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🚀 Why this matters?

These concepts are used in:

• Machine Learning Model training
• Deep Learning (Neural Networks)
• PCA / Dimensionality Reduction
• Matrix transformations

Today was a strong foundation day 💪

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📂 GitHub Code

🔗 https://github.com/ramyacse21/numpy_workspace/blob/main/linear%20algebra.py
Example format:

GitHub Project: https://github.com/ramyacse21/your-repo-link
#RamyaAnalyticsJourney
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