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3Blue1Brown
Linear combinations, span, and basis vectors: Essence of Linear Algebra - Part 2 of 15
Some foundational ideas in linear algebra: Span, linear combinations, and linear dependence.
Professor Dave Explains
Linear Second-Order Differential Equations Part 1: Homogeneous Case
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,...
Curated Video
Data Science and Machine Learning (Theory and Projects) A to Z - Mathematical Foundation: Vector Space
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)...
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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)...
Curated Video
Data Science and Machine Learning (Theory and Projects) A to Z - Mathematical Foundation: Linear Independence
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...
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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...
Curated Video
Data Science and Machine Learning (Theory and Projects) A to Z - Mathematical Foundation: Basis and Dimensions
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...
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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...
Khan Academy
Khan Academy: Linear Algebra: Span and Linear Independence Example
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]
Khan Academy
Khan Academy: Linear Algebra: More on Linear Independence
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...
Khan Academy
Khan Academy: Linear Algebra: Null Space 3: Relation to Linear Independence
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...
Khan Academy
Khan Academy: Linear Algebra: Introduction to Linear Independence
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]
Khan Academy
Khan Academy: Linear Algebra: Proof of Formula for Determining Eigenvalues
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...
Khan Academy
Khan Academy: Linear Algebra: Span and Linear Independence Example
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]
Khan Academy
Khan Academy: Eigen Everything: Proof of Formula for Determining Eigenvalues
Proof of formula for determining Eigenvalues.
Khan Academy
Khan Academy: Showing Relation Between Basis Cols and Pivot Cols
This video shows that linear independence of pivot columns implies linear independence of the corresponding columns in the original equation.