Proof of the Rank-Nullity Theorem, one of the cornerstones of linear algebra. Intuitively, it says that the rank and the nullity of a linear transformation are related: the more vectors T sends to 0, the smaller its range. The proof is especially elegant and uses important concepts in line
From playlist Linear Transformations
Definitions of null space, injectivity, range, and surjectivity. Fundamental theorem of linear maps. Consequences for systems of linear equations.
From playlist Linear Algebra Done Right
Overview of null hypothesis, examples of null and alternate hypotheses, and how to write a null hypothesis statement.
From playlist Hypothesis Tests and Critical Values
Prove a Null Space is a Subspace
This video provides a basic proof that a null space is a subspace.
From playlist Column and Null Space
Null space of a matrix example
In today's lecture I work through an example to show you a well-known pitfall when it comes to the null space of a matrix. In the example I show you how to create the special cases and how to use them to represent the null space. There is also a quick look at the NullSpace function in Ma
From playlist Introducing linear algebra
Null points and null lines | Universal Hyperbolic Geometry 12 | NJ Wildberger
Null points and null lines are central in universal hyperbolic geometry. By definition a null point is just a point which lies on its dual line, and dually a null line is just a line which passes through its dual point. We extend the rational parametrization of the unit circle to the proj
From playlist Universal Hyperbolic Geometry
53 - The rank-nullity theorem revisited
Algebra 1M - international Course no. 104016 Dr. Aviv Censor Technion - International school of engineering
From playlist Algebra 1M
Linear Algebra - Lecture 32 - Dimension, Rank, and Nullity
In this video, I define the dimension of a subspace. I also prove the fact that any two bases of a subspace must have the same number of vectors, which guarantees that dimension is well-defined. Finally, I define the rank and nullity of a matrix, and explain the Rank-Nullity Theorem.
From playlist Linear Algebra Lectures
Linear Transformations -- Abstract Linear Algebra 13
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From playlist Abstract Linear Algebra
WildLinAlg17: Rank and Nullity of a Linear Transformation
We begin to discuss linear transformations involving higher dimensions (ie more than three). The kernel and the image are important spaces, or properties of vectors, associated to a linear transformation. The corresponding dimensions are the nullity and the rank, and they satisfy a simple
From playlist A first course in Linear Algebra - N J Wildberger
Algebra 1M - international Course no. 104016 Dr. Aviv Censor Technion - International school of engineering
From playlist Algebra 1M
Algebra 1M - international Course no. 104016 Dr. Aviv Censor Technion - International school of engineering
From playlist Algebra 1M
Algebra 1M - international Course no. 104016 Dr. Aviv Censor Technion - International school of engineering
From playlist Algebra 1M
Invertible Matrix Theorem -- Abstract Linear Algebra 16
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From playlist Abstract Linear Algebra
Null Space: Is a Vector in a Null Space? Find a Basis for a Null Space
This video explains how to determine if a vector is in a null space and how to find a basis for a null space.
From playlist Column and Null Space
In this video I start to discuss the idea of the null space of a matrix. In these situations, the right-hand side of all the equations in the linear system is equal to zero. There is the trivial solution, where all the elements of the solution is zero. We are more interested in the spec
From playlist Introducing linear algebra
In this video, I show that two vector spaces are isomorphic if and only if they have the same dimension. This is an important fact in linear algebra. The proof is very cute and uses the linear extension theorem which I talked about in another video. Enjoy! Linear Extension Theorem https:/
From playlist Linear Transformations