Linear Algebra for Machine Learning: 2 Resources

If you're learning Machine Learning or Deep Learning, you don't need 20 different resources to learn Linear Algebra.
You can start with two excellent resources:

• 🎓 3Blue1Brown - Essence of Linear Algebra for visual intuition.
• 🎓 MIT OpenCourseWare - Gilbert Strang for a more structured and in-depth study.

The real problem is not finding Linear Algebra resources. There are too many of them. You can start with Vectors, jump to Matrices, and suddenly find yourself trying to understand Eigenvalues and SVD without knowing why these concepts matter.
A better approach is to learn the ideas in the right order.

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🎓 1. 3Blue1Brown - Essence of Linear Algebra​

If Linear Algebra feels abstract, start here.
The Essence of Linear Algebra series by 3Blue1Brown focuses heavily on visual explanations. Instead of memorizing formulas first, you get an intuitive understanding of what the mathematics represents.

You'll encounter concepts such as:

• Vectors
• Linear Combinations
• Matrices
• Linear Transformations
• Dot Products
• Eigenvalues
• Eigenvectors

The biggest advantage is the focus on visual intuition.
For example, a matrix isn't just a rectangular grid of numbers. It can represent a transformation that changes vectors in a specific way.
That kind of intuition becomes extremely useful when you later encounter matrices throughout Machine Learning.
💡 Use this resource to understand the "why" before worrying too much about the calculations.

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🎓 2. MIT OpenCourseWare - Gilbert Strang​

Once you have a basic visual understanding, move to a more systematic treatment of Linear Algebra.
MIT's 18.06 Linear Algebra course, associated with Professor Gilbert Strang, covers many of the mathematical foundations you'll need.

Topics include:

• Systems of Linear Equations
• Matrix Operations
• Vector Spaces
• Basis and Dimension
• Orthogonality and Projections
• Least Squares
• Eigenvalues and Eigenvectors
• Singular Value Decomposition (SVD)

The course also provides lectures and supporting materials that make it useful for deeper study and practice.
✍️ This is where you should spend more time solving problems instead of only watching videos.

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🔄 The Best Way to Use Both Resources​

Don't watch both resources from beginning to end without a plan.
A more effective workflow is:

1. 👁️ Understand the concept with 3Blue1Brown.
2. 📚 Study the same concept more deeply with MIT/Strang.
3. ✍️ Solve problems by hand.
4. 💻 Apply the concept using Python and NumPy.

For example, when learning vectors, don't stop after watching an explanation.
Try creating vectors yourself and performing operations such as addition and the dot product with NumPy.

import numpy as np

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

print(a + b)
print(np.dot(a, b))

The goal isn't to memorize the syntax.
The goal is to connect the mathematical operation with what you're doing in code.

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🧠 Why Linear Algebra Matters for Machine Learning​

Linear Algebra becomes important because Machine Learning models work heavily with numerical representations of data.
A simplified view looks like this:
Data → Vectors → Matrices → Transformations → Machine Learning → Neural Networks
For example, you'll eventually see equations such as:

y = Wx + b

At first, this might look like nothing more than a mathematical formula.

But after learning Linear Algebra, you should be able to recognize that:

• x can represent an input vector.
• W can represent a matrix of weights.
• b can represent a bias vector.
• Wx represents a matrix-vector operation.
• y represents the resulting output.

That's a much more useful understanding than simply knowing how to multiply two matrices.

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🐍 Practice Linear Algebra with Python and NumPy​

You don't need to turn every mathematical exercise into a programming project.
Instead, use Python and NumPy to reinforce concepts you've already studied.
For example, after learning matrix multiplication:

import numpy as np

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

B = np.array([
[5, 6],
[7, 8]
])

C = A @ B

print(C)

Then compare the result with the calculation you performed by hand.

This creates a useful connection between:
Mathematical notation → Manual calculation → Python implementation
That connection becomes increasingly valuable as you move into Machine Learning and Deep Learning.

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⚠️ Don't Try to Learn Everything at Once​

You don't need to master every Linear Algebra topic before writing your first line of Machine Learning code.
Focus on building a solid foundation first.
A practical progression is:

1. Vectors
2. Vector Operations
3. Dot Product
4. Matrices
5. Matrix Multiplication
6. Linear Transformations
7. Systems of Linear Equations
8. Vector Spaces
9. Basis and Dimension
10. Orthogonality and Projections
11. Eigenvalues and Eigenvectors
12. Least Squares
13. SVD

You can then revisit specific topics when they appear in Machine Learning.

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🎯 What You Should Actually Aim For​

The goal isn't to memorize 100 Linear Algebra formulas.
You want to reach the point where you see something like:

y = Wx + b

in a Machine Learning model and think:
"I understand what's happening here."
That's when Linear Algebra starts becoming more than a difficult college subject.
It becomes a mathematical language that helps you understand how Machine Learning and Deep Learning models work.

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📌 A Simple Learning Strategy​

If you're starting from zero, keep it simple:
3Blue1Brown → MIT/Strang → Practice → NumPy → Machine Learning
Use 3Blue1Brown to build intuition.
Use MIT/Strang to develop a stronger mathematical foundation.
Solve problems yourself instead of only watching lectures.
Then use Python and NumPy to connect the mathematics to real code. 💻
You don't need to collect dozens of courses before starting.
Start with two resources, follow a clear order, and practice what you learn.
The search for the "perfect" Linear Algebra course can easily become a replacement for actually studying it.