Oxford Linear Algebra: Linear Transformations Explained
University of Oxford mathematician Dr Tom Crawford introduces the concept of a Linear Transformation with a motivation for the definition and several worked examples. Check out ProPrep with a 30-day free trial: https://www.proprep.uk/info/TOM-Crawford
Links to the other videos mentioned:
Vector Space Axioms - • Oxford Linear Algebra: Subspace Test
Test your understanding of the content covered in the video with some practice exercises courtesy of ProPrep. You can download the workbooks and solutions for free here: https://api.proprep.com/course/downlo...
You can also find several video lectures from ProPrep explaining the content covered in the video here: https://www.proprep.com/courses/all/l...
As with all modules on ProPrep, each set of videos contains lectures, worked examples and full solutions to all exercises.
The video begins with the formal mathematical definition of a linear transformation and how their properties relate to those of a vector space. There is also a discussion as to how linear maps ensure that the structure of a vector space is preserved.
An alternative definition for a linear transformation is then introduced, which is often used to check whether or not a given map is indeed linear. We also see how a linear transformation must always map the zero vector in the starting space to the zero vector of the final space. A generalised application to a basis of a vector space is also briefly mentioned (this will be discussed further in the next video on the Rank-Nullity Theorem.)
Several examples of linear maps are looked at in detail, including multiplication by a matrix, differentiation, and three explicit maps in R3. The final example re-introduces the concept of a direct sum (as seen in the previous video) and how it can be used to define a projection map.
Watch the other videos from the Oxford Linear Algebra series at the links below.
Solving Systems of Linear Equations using Elementary Row Operations (ERO’s): • Oxford Linear Algebra: Elementary Row...
Calculating the inverse of 2x2, 3x3 and 4x4 matrices: • Oxford Linear Algebra: How to find a ...
What is the Determinant Function: • Oxford Linear Algebra: What is the De...
The Easiest Method to Calculate Determinants: • Oxford Linear Algebra: The Easiest Me...
Eigenvalues and Eigenvectors Explained: • Oxford Linear Algebra: Eigenvalues an...
Spectral Theorem Proof: • Oxford Linear Algebra: Spectral Theor...
Vector Space Axioms: • Oxford Linear Algebra: What is a Vect...
Subspace Test: • Oxford Linear Algebra: Subspace Test
Basis, Spanning and Linear Independence: • Oxford Linear Algebra: Basis, Spannin...
Dimension Formula: • Oxford Linear Algebra: Dimension Form...
Direct Sum: • Oxford Linear Algebra: Direct Sum of ...
Produced by Dr Tom Crawford at the University of Oxford. Tom is an Early-Career Teaching and Outreach Fellow at St Edmund Hall: https://www.seh.ox.ac.uk/people/tom-c...
For more maths content check out Tom's website https://tomrocksmaths.com/
You can also follow Tom on Facebook, Twitter and Instagram @tomrocksmaths.
/ tomrocksmaths
/ tomrocksmaths
/ tomrocksmaths
Get your Tom Rocks Maths merchandise here:
https://beautifulequations.net/collec...
Auf dieser Seite können Sie das Online-Video Oxford Linear Algebra: Linear Transformations Explained mit der Dauer stunde minuten sekunde in guter Qualität ansehen, das der Benutzer Tom Rocks Maths 01 Januar 1970 hochgeladen hat, den Link mit Freunden und Bekannten teilen, dieses Video wurde auf Youtube bereits 17,491 Mal angesehen und es wurde von 466 den Zuschauern gefallen. Viel Spaß beim Betrachtenden Zuschauern gefallen!
