Instructional Video9:58
3Blue1Brown

Linear combinations, span, and basis vectors: Essence of Linear Algebra - Part 2 of 15

12th - Higher Ed
Some foundational ideas in linear algebra: Span, linear combinations, and linear dependence.
Instructional Video9:49
Professor Dave Explains

Linear Second-Order Differential Equations Part 1: Homogeneous Case

9th - Higher Ed
After a number of tutorials covering first-order differential equations, it's time to start tackling second-order differential equations. These contain a second derivative term, and they are quite useful in physics. To introduce these,...
Instructional Video12:25
Professor Dave Explains

Linear Independence

9th - Higher Ed
Defining linear independence.
Instructional Video12:18
Curated Video

Data Science and Machine Learning (Theory and Projects) A to Z - Mathematical Foundation: Vector Space

Higher Ed
In this video, we will cover vector space.
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This clip is from the chapter "Machine Learning: Feature Engineering and Dimensionality Reduction with Python" of the series "Data Science and Machine Learning (Theory and Projects)...
Instructional Video6:29
Curated Video

Data Science and Machine Learning (Theory and Projects) A to Z - Mathematical Foundation: Linear Independence

Higher Ed
In this video, we will cover linear independence.
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This clip is from the chapter "Machine Learning: Feature Engineering and Dimensionality Reduction with Python" of the series "Data Science and Machine Learning (Theory and...
Instructional Video10:14
Curated Video

Data Science and Machine Learning (Theory and Projects) A to Z - Mathematical Foundation: Basis and Dimensions

Higher Ed
In this video, we will cover basis and dimensions.
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This clip is from the chapter "Machine Learning: Feature Engineering and Dimensionality Reduction with Python" of the series "Data Science and Machine Learning (Theory and...
Instructional Video9:35
Professor Dave Explains

Basis and Dimension

9th - Higher Ed
Defining basis and dimension.
Instructional Video
Khan Academy

Khan Academy: Linear Algebra: Span and Linear Independence Example

9th - 10th
Video shows an example of proving that a particular linear combination of 3 vectors in R3 spans R3. Relates this to linearly independent and linearly dependent vectors. [16:53]
Instructional Video
Khan Academy

Khan Academy: Linear Algebra: More on Linear Independence

9th - 10th
Video expands the examples of linearly independent and linearly dependent vectors shown in the previous video to give a formal definition of linearly dependent vectors. Shows a proof of the definition and then gives an example of using...
Instructional Video
Khan Academy

Khan Academy: Linear Algebra: Null Space 3: Relation to Linear Independence

9th - 10th
Video reviews what the null space of a matrix is and how to calculate it, then relates it to linear independence. Shows that if the vectors are linearly independent then the null space is the zero vector. Also shows that if the null...
Instructional Video
Khan Academy

Khan Academy: Linear Algebra: Introduction to Linear Independence

9th - 10th
Video explains what linearly dependent vectors and linearly independent vectors are. Shows visual representations to help explain the concept and relates it to the span of the linear combination of the vectors. [15:46]
Instructional Video
Khan Academy

Khan Academy: Linear Algebra: Proof of Formula for Determining Eigenvalues

9th - 10th
Video beginning the process of finding eigenvectors and their eigenvalues by manipulating the equation for finding a transformation where the result is an eigenvector. Includes review of null space and linear independence and dependence...
Instructional Video
Khan Academy

Khan Academy: Linear Algebra: Span and Linear Independence Example

9th - 10th
Video shows an example of proving a particular linear combination of 3 vectors in R3 spans R3. Relates this to linearly independent and linearly dependent vectors. [16:53]
Instructional Video
Instructional Video
Khan Academy

Khan Academy: Showing Relation Between Basis Cols and Pivot Cols

9th - 10th
This video shows that linear independence of pivot columns implies linear independence of the corresponding columns in the original equation.