_    ___ ___      _                               
   / \  |_ _/ _ \ ___| |_ _ __ ___  __ _ _ __ ___  ___
  / _ \  | | | | / __| __| '__/ _ \/ _` | '_ ` _ \/ __|
 / ___ \ | | |_| \__ \ |_| | |  __/ (_| | | | | | \__ \
/_/   \_\___\___/|___/\__|_|  \___|\__,_|_| |_| |_|___/

Invidious > Channel > MathTheBeautiful

MathTheBeautiful	93100 subscribers    RSS
View channel on YouTube Videos Playlists

YT 8 minutes 13 seconds MathTheBeautiful Linear Algebra 15b: What Makes a Transformation Linear? YT 20 minutes 6 seconds MathTheBeautiful Linear Algebra 15c: The Reflection Transformation and Introduction to Eigenvalues YT 10 minutes 31 seconds MathTheBeautiful Linear Algebra 15d: The Projection Transformation

YT 9 minutes 3 seconds MathTheBeautiful Linear Algebra 15e: The Rotation Transformation YT 3 minutes 42 seconds MathTheBeautiful Linear Algebra 15f: The Transformation of Translation YT 17 minutes 32 seconds MathTheBeautiful Linear Algebra 15g: Geometric Transformation in Space, As Opposed to on the Plane

YT 16 minutes 10 seconds MathTheBeautiful Linear Algebra 15h: The Derivative as a Linear Transformation YT 6 minutes 34 seconds MathTheBeautiful Linear Algebra 15i: Dilation as a Linear Transformation YT 8 minutes 6 seconds MathTheBeautiful Linear Algebra 15j: Example of Nonlinear Transformations of Functions

YT 9 minutes 25 seconds MathTheBeautiful Linear Algebra 15k: A Linear Transformation in ℝⁿ YT 9 minutes 54 seconds MathTheBeautiful Linear Algebra 15L: Another Linear Transformation in ℝⁿ YT 7 minutes 20 seconds MathTheBeautiful Linear Algebra 15m: All Transformations in ℝⁿ Can Be Represented by Matrix Products

YT 2 minutes 42 seconds MathTheBeautiful Linear Algebra 15m+: The Identity Crisis, I Mean, Transformation YT 12 minutes 7 seconds MathTheBeautiful Linear Algebra 15n: Why Eigenvalues and Eigenvectors Are So Important! YT 13 minutes 13 seconds MathTheBeautiful Linear Algebra 15o: The Null Space of a Linear Transformation

YT 18 minutes 29 seconds MathTheBeautiful Linear Algebra 15p: The Inverse of a Linear Transformation YT 20 minutes 34 seconds MathTheBeautiful Linear Algebra 16a: The Eigenvalue Algorithm YT 5 minutes 23 seconds MathTheBeautiful Linear Algebra 16b: Algebraic Derivation of the Eigenvalue Algorithm

YT 8 minutes MathTheBeautiful Linear Algebra 16c: Determining Eigenvalues and Eigenvectors, a Detailed Example YT 14 minutes 46 seconds MathTheBeautiful Linear Algebra 16c1: The Sum is the Trace and the Product Is the Determinant of the Matrix YT 3 minutes 55 seconds MathTheBeautiful Linear Algebra 16c2: A and Aᵀ Have the Same Eigenvalues

YT 3 minutes 22 seconds MathTheBeautiful Linear Algebra 16d: Eigenvalues and Eigenvectors - A 2x2 Example YT 5 minutes 3 seconds MathTheBeautiful Linear Algebra 16e: Eigenvalues and Eigenvectors Example with Radicals YT 1 minute 9 seconds MathTheBeautiful Linear Algebra 16f: Eigenvalues and Eigenvectors Example - No Real Eigenvalues

YT 4 minutes 46 seconds MathTheBeautiful Linear Algebra 16g: Eigenvalues and Eigenvectors Example - A 3x3 Triangular Matrix YT 8 minutes 33 seconds MathTheBeautiful Linear Algebra 16h1: Repeated Eigenvalues and the Geometric Mulitplicity YT 3 minutes 37 seconds MathTheBeautiful Linear Algebra 16h2: Repeated Eigenvalues and the Algebraic Multiplicity

YT 4 minutes 33 seconds MathTheBeautiful Linear Algebra 16h3: Algebraic Multiplicity Matches Geometric Multiplicty YT 10 minutes 54 seconds MathTheBeautiful Linear Algebra 16h4: Defective Matrices YT 4 minutes 58 seconds MathTheBeautiful Linear Algebra 16h5: Defective Transformations?

YT 7 minutes 36 seconds MathTheBeautiful Linear Algebra 16h6: Generalized Eigenvectors YT 2 minutes 47 seconds MathTheBeautiful Linear Algebra 16h7: Generalized Eigenvectors Example YT 6 minutes 28 seconds MathTheBeautiful Linear Algebra 16h8: Defective Transformations!

YT 5 minutes 32 seconds MathTheBeautiful Linear Algebra 16j: Eigenvalues and Eigenvectors of the Square and the Inverse YT 4 minutes 50 seconds MathTheBeautiful Linear Algebra 16k: Eigenvalues, Eigenvectors and the Similarity Transformation YT 5 minutes 46 seconds MathTheBeautiful Linear Algebra 16L: Similarity Transformations Preserve the Trace and the Determinant

YT 10 minutes 11 seconds MathTheBeautiful Linear Algebra 16m: Eigenvalues, Eigenvectors and the Square Root of a Matrix YT 12 minutes 42 seconds MathTheBeautiful Linear Algebra 16n: Every Matrix Satisfies Its Characteristic Equation YT 5 minutes 19 seconds MathTheBeautiful Linear Algebra 17a: Easy Eigenvalues - Diagonal Matrix

YT 4 minutes 19 seconds MathTheBeautiful Linear Algebra 17b: Easy Eigenvalues - Diagonal Entry - A Single Nonzero Entry in a Column YT 2 minutes 54 seconds MathTheBeautiful Linear Algebra 17c: Easy Eigenvalues - Equal Sums of Rows or Columns YT 5 minutes 45 seconds MathTheBeautiful Linear Algebra 17d: Easy Eigenvalues - Nontrivial Null Space

YT 4 minutes 23 seconds MathTheBeautiful Linear Algebra 17e: Easy Eigenvalues - The Trace YT 3 minutes 44 seconds MathTheBeautiful Linear Algebra 17f: Easy Eigenvalues - The Determinant YT 3 minutes 32 seconds MathTheBeautiful Linear Algebra 17g: Easy Eigenvalues - The Transpose

YT 6 minutes 42 seconds MathTheBeautiful Linear Algebra 17h: Easy Eigenvalues - The Block Diagonal Structure YT 2 minutes 51 seconds MathTheBeautiful Linear Algebra 17i: Easy Eigenvalues - The Grand Finale YT 5 minutes 26 seconds MathTheBeautiful Linear Algebra 17j: Constructing a Matrix with a Prescribed Spectrum

YT 10 minutes 23 seconds MathTheBeautiful Linear Algebra 18a: Introduction to the Eigenvalue Decomposition YT 4 minutes 32 seconds MathTheBeautiful Linear Algebra 18b: A Worked out Eigenvalue Decomposition Example YT 9 minutes 50 seconds MathTheBeautiful Linear Algebra 18c: An Important Implication of the Eigenvalue Decomposition

YT 10 minutes 11 seconds MathTheBeautiful Linear Algebra 18d: The Eigenvalue Decomposition and Powers of a Matrix YT 28 minutes 50 seconds MathTheBeautiful Linear Algebra 18e: The Eigenvalue Decomposition and Fibonacci Numbers YT 13 minutes 37 seconds MathTheBeautiful Linear Algebra 19a: Component Spaces - What They Are for and When to Use Them

YT 15 minutes 21 seconds MathTheBeautiful Linear Algebra 19b: Component Spaces - Doing It Right! YT 16 minutes 41 seconds MathTheBeautiful Linear Algebra 19c: Illustration of Component Spaces by a Sum of Geometric Vectors YT 8 minutes 14 seconds MathTheBeautiful Linear Algebra 19d: Illustration of Component Spaces by a Sum of Polynomials

YT 4 minutes 50 seconds MathTheBeautiful Linear Algebra 19e: Illustration of Component Spaces by a Sum of Vectors in ℝⁿ YT 14 minutes 34 seconds MathTheBeautiful Linear Algebra 19f: The Heart of Component Spaces - Matrix Representation of a Linear Tranformation YT 6 minutes 22 seconds MathTheBeautiful Linear Algebra 19g: Matrix Representation of a LT - the Algorithm Works!

YT 9 minutes 7 seconds MathTheBeautiful Linear Algebra 19h: Matrix Representation of a Linear Transformation - Alternative Basis YT 8 minutes 36 seconds MathTheBeautiful Linear Algebra 19i: Bad Basis! Bad Basis! Go to Your Room! YT 10 minutes 19 seconds MathTheBeautiful Linear Algebra 19j: Matrix Representation of a Linear Transformation - Polynomials

YT 12 minutes 40 seconds MathTheBeautiful Linear Algebra 19k: Matrix Representation of a Linear Transformation - Vectors in ℝⁿ YT 3 minutes 46 seconds MathTheBeautiful Linear Algebra 19L: Matrix Representation of a LT - Vectors in ℝⁿ, Standard Basis YT 11 minutes 12 seconds MathTheBeautiful Linear Algebra 19m: Matrix Representation of a LT - Vectors in ℝⁿ, Eigenbasis

YT 8 minutes 47 seconds MathTheBeautiful Linear Algebra 19n: Matrix Representation of a LT - Vectors in ℝⁿ, Second Example YT 5 minutes 23 seconds MathTheBeautiful Linear Algebra 19o: Matrix Representation of a LT - Better than an Eigenbasis? YT 7 minutes 28 seconds MathTheBeautiful Linear Algebra 19p: Proof that Eigenbasis Yields a Diagonal Matrix

YT 5 minutes 58 seconds MathTheBeautiful Linear Algebra 19q: Matrix Representation of a LT - The Identity Transformation YT 14 minutes 3 seconds MathTheBeautiful Linear Algebra 19r: Translations, or How to Represent Nonlinear Transformations by Matrix Products YT 10 minutes 18 seconds MathTheBeautiful Linear Algebra 19s: A Moment for Reflection... Eigenvalues

YT 9 minutes 13 seconds MathTheBeautiful Linear Algebra 19t: I Once Was Blind, but Now Am Dilated YT 8 minutes 39 seconds MathTheBeautiful Linear Algebra 20a: Introduction to Transformations (Mostly Linear) in the Plane and in the 3D Space YT 16 minutes 45 seconds MathTheBeautiful Linear Algebra 20b: Length Expressed in Terms of Components of a Vector

YT 8 minutes 22 seconds MathTheBeautiful Linear Algebra 20c: Length Expressed in a non-Cartesian Basis YT 17 minutes 31 seconds MathTheBeautiful Linear Algebra 20d: Length Preserving Linear Transformations and Orthogonal Matrices YT 11 minutes 28 seconds MathTheBeautiful Linear Algebra 20e: Proof that Length Preservation Implies the Orthogonal Matrix Property

YT 2 minutes 37 seconds MathTheBeautiful Linear Algebra 20f: The Product of Two Orthogonal Matrices Is Itself an Orthogonal Matrix YT 15 minutes 54 seconds MathTheBeautiful Linear Algebra 20g: The Dot Product - One of the Most Brilliant Ideas in All of Linear Algebra YT 15 minutes 11 seconds MathTheBeautiful Linear Algebra 20h: The Key Properties of the Dot Product

YT 8 minutes 19 seconds MathTheBeautiful Linear Algebra 20i: Component Representation of the Dot Product, as if You Don't Know It Already YT 19 minutes 18 seconds MathTheBeautiful Linear Algebra 20j: The Dot Product, Matrix Multiplication, and the Magic of Orthogonal Matrices YT 12 minutes 23 seconds MathTheBeautiful Linear Algebra 20k: Two Derivations of the Dot Product Component Space Expression

YT 8 minutes 39 seconds MathTheBeautiful Linear Algebra 20L: The Dot Product in Non-Cartesian Bases, the Gram Matrix or the Metric YT 14 minutes 29 seconds MathTheBeautiful Linear Algebra 21a: Rigid Transformations YT 10 minutes 46 seconds MathTheBeautiful Linear Algebra 21b: Rotations, Plane and Simple!

YT 21 minutes 22 seconds MathTheBeautiful Linear Algebra 21c: Rotation Matrices - Or Why You Should Love Trig YT 12 minutes 22 seconds MathTheBeautiful Linear Algebra 21d: Rotation Matrices in a Non-Cartesian Basis YT 12 minutes 5 seconds MathTheBeautiful Linear Algebra 21e: What All 2x2 Orthogonal Matrices Look Like

YT 12 minutes 23 seconds MathTheBeautiful Linear Algebra 21f: Rotation Matrices in 3D for Rotations with respect to the Coordinate Axes YT 17 minutes 13 seconds MathTheBeautiful Linear Algebra 21g: Euler Angles and a Short Tribute to Leonhard Euler YT 12 minutes 39 seconds MathTheBeautiful Linear Algebra 21h: The Matrix that Represents an Arbitrary Rotation in 3D

YT 6 minutes 45 seconds MathTheBeautiful Linear Algebra 21i: How to Represent a Rotation with respect to an Arbitrary Axis YT 5 minutes 34 seconds MathTheBeautiful Linear Algebra 21j: Two Geometric Interpretations of Orthogonal Matrices YT 14 minutes 55 seconds MathTheBeautiful Linear Algebra 22a: Introduction to Orthoscaling (aka Symmetric) Transformations

YT 8 minutes 11 seconds MathTheBeautiful Linear Algebra 22b: Orthoscaling Transformations Are (Sometimes) Represented by Symmetric Matrices YT 16 minutes 41 seconds MathTheBeautiful Linear Algebra 22c: Symmetric Matrices Have Orthogonal Eigenvectors YT 4 minutes 48 seconds MathTheBeautiful Linear Algebra 22d: Symmetric Matrices (Even with Repeated Eigenvalues) Have Orthogonal Eigenvectors

YT 4 minutes 20 seconds MathTheBeautiful Linear Algebra 22e: The Symmetric Property as a New Eigenvalue Giveaway YT 10 minutes 57 seconds MathTheBeautiful Linear Algebra 22f: Symmetric Matrices and the Eigenvalue Decomposition YT 5 minutes 4 seconds MathTheBeautiful Linear Algebra 22g: Geometric Interpretation of the Eigenvalue Decomposition for Symmetric Matrices

YT 2 minutes 9 seconds MathTheBeautiful Linear Algebra 22h: Is the Inverse of a Symmetric Matrix Itself Symmetric? YT 11 minutes 51 seconds MathTheBeautiful Linear Algebra 22i: Symmetric Matrices and the LDU Decomposition YT 8 minutes 40 seconds MathTheBeautiful Linear Algebra 22j: The Cholesky Decomposition and a Tribute to Land Surveyors

YT 9 minutes 55 seconds MathTheBeautiful Linear Algebra 23a: Polar Decomposition - A Product of an Orthogonal and Symmetric Matrices YT 14 minutes 59 seconds MathTheBeautiful Linear Algebra 23b: How to Determine the Matrices Q and S in the Polar Decomposition YT 3 minutes 15 seconds MathTheBeautiful Linear Algebra 23c: A Worked out Polar Decomposition Example

YT 3 minutes 52 seconds MathTheBeautiful Linear Algebra 23d: Demonstration That AᵀA and AAᵀ Have Identical Eigenvalues YT 6 minutes 25 seconds MathTheBeautiful Linear Algebra 23e: Reversing the Multiplicative Terms in the Polar Decomposition YT 12 minutes 1 second MathTheBeautiful Linear Algebra 23f: Introducing the Celebrated Singular Value Decomposition (SVD)

YT 3 minutes 50 seconds MathTheBeautiful Linear Algebra 23g: SVD Proof That the Orthogonal Matrices in Alternative Polar Decompositions Match YT 8 minutes 23 seconds MathTheBeautiful Linear Algebra Proofs 15b: Eigenvectors with Different Eigenvalues Are Linearly Independent