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Lecture
StateSpace ControlCanonical: Canonical Forms
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Related lectures (45)
State-Space Representation: Controllability and Observability
Explores state-space representation, controllability, observability, and regulator calculation using the Ackermann method.
Observability and Controllability
Explores observability and controllability in linear systems, emphasizing the significance of input decoupling for observability.
State-Space Representation: Structure Theorem
Covers the structure theorem for state-space representations and companion forms.
Reducing an Application
Covers the reduction of an application, finding reduced forms of matrices, diagonalizability, and polynomial roots.
Diagonalization of Linear Transformations
Covers the diagonalization of linear transformations in R^3, exploring properties and examples.
System Equivalence
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Matrix to Density Operator
Explains the transformation from a matrix to the density operator in quantum physics.
Change of Basis: Motivation
MOOC: Linear Algebra (Part 2)
Explores the motivation behind change of basis in linear algebra, emphasizing the importance of selecting the right basis.
Diagonalization Techniques: Jacobi Method
Explores the Jacobi method and diagonalization techniques, including similarity transformation, power methods, and QR decomposition.
Characteristic Polynomials and Similar Matrices
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Explores characteristic polynomials, similarity of matrices, and eigenvalues in linear transformations.
Matrix Operations: Composition and Product
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Covers the composition and product of matrices, including matrix multiplication.
Linear Transformations: Injective and Surjective
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Explores injective and surjective linear transformations, kernel, image, and matrix operations.
Matrix Multiplication: Applications and Properties
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Covers matrix multiplication, properties, and inverses in linear algebra.
Change of Frames in 2D
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Explores changing frames in 2D through translations, rotations, and the introduction of a transformation matrix U.
Elementary Matrices and Matrix Factorization
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Covers elementary matrices, matrix factorization, and LU decomposition.
Matrix Inversibility: Determining and Calculating
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Covers matrix invertibility, determining if a matrix is invertible, calculating its inverse, and elementary matrices.
Linear Algebra: Matrices and Inverses
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Explores matrices, inverses, and their applications in linear algebra, emphasizing composition and transformation properties.
Matrix Transformation: Base Change
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Explains matrix transformation in different bases and how to find the new matrix.
Linear Algebra: Matrix Operations
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Explores the equivalence between different properties of linear transformations represented by matrices and various matrix operations.
Base Changes and Rank
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Explores base changes, bijective linear applications, matrix transformations, and dimensions of kernel and image spaces.
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