Search Results (2)

Save

Please log in to save materials.

View
Selected filters:
  • Row Operations
Linear Algebra II
Conditions of Use:
Read the Fine Print
Rating

Linear Algebra is both rich in theory and full of interesting applications; ... More

Linear Algebra is both rich in theory and full of interesting applications; in this course the student will try to balance both. This course includes a review of topics learned in Linear Algebra I. Upon successful completion of this course, the student will be able to: Solve systems of linear equations; Define the abstract notions of vector space and inner product space; State examples of vector spaces; Diagonalize a matrix; Formulate what a system of linear equations is in terms of matrices; Give an example of a space that has the Archimedian property; Use the Euclidean algorithm to find the greatest common divisor; Understand polar form and geometric interpretation of the complex numbers; Explain what the fundamental theorem of algebra states; Determine when two matrices are row equivalent; State the Fredholm alternative; Identify matrices that are in row reduced echelon form; Find a LU factorization for a given matrix; Find a PLU factorization for a given matrix; Find a QR factorization for a given matrix; Use the simplex algorithm; Compute eigenvalues and eigenvectors; State Shur's Theorem; Define normal matrices; Explain the composition and the inversion of permutations; Define and compute the determinant; Explain when eigenvalues exist for a given operator; Normal form of a nilpotent operator; Understand the idea of Jordan blocks, Jordan matrices, and the Jordan form of a matrix; Define quadratic forms; State the second derivative test; Define eigenvectors and eigenvalues; Define a vector space and state its properties; State the notions of linear span, linear independence, and the basis of a vector space; Understand the ideas of linear independence, spanning set, basis, and dimension; Define a linear transformation; State the properties of linear transformations; Define the characteristic polynomial of a matrix; Define a Markov matrix; State what it means to have the property of being a stochastic matrix; Define a normed vector space; Apply the Cauchy Schwarz inequality; State the Riesz representation theorem; State what it means for a nxn matrix to be diagonalizable; Define Hermitian operators; Define a Hilbert space; Prove the Cayley Hamilton theorem; Define the adjoint of an operator; Define normal operators; State the spectral theorem; Understand how to find the singular-value decomposition of an operator; Define the notion of length for abstract vectors in abstract vector spaces; Define orthogonal vectors; Define orthogonal and orthonormal subsets of R^n; Use the Gram-Schmidt process; Find the eigenvalues and the eigenvectors of a given matrix numerically; Provide an explicit description of the Power Method. (Mathematics 212) Less

More
Subject:
Algebra
Functions
Material Type:
Assessments
Full Course
Homework and Assignments
Readings
Syllabi
Textbooks
Provider:
The Saylor Foundation
Provider Set:
Saylor Foundation
Less
2002 gnirpS ,ngiseD gnireenignE liviC ot noitcudortnI
Rating

.)310.1( tcejbus ngised enotspac eht dna )150.1 ,140.1 ,130.1( stcejbus ngised aera ... More

.)310.1( tcejbus ngised enotspac eht dna )150.1 ,140.1 ,130.1( stcejbus ngised aera ytlaiceps tneuqesbus eht ni desu si hcihw decudortni si esac ngised egral A .naps efil detcepxe dna ,srotcaf laicos dna cimonoce ,tnemnorivne larutan ,tnemnorivne tliub gnitsixe eht fo noitaredisnoc sa llew sa sehcaorppa lacinhcet snrecnoc ylticilpxe ngised tcejorP .)sdaor dna segdirb ,sgnidliub ,.g.e( seitilicaf tliub no sisahpme na htiw ,sesac ngised lareves sedulcnI .gnireenigne livic ni secitcarp dna seussi ngised sa llew sa ,gnivlos-melborp evitaerc dna ngised gnireenigne fo seuqinhcet dna ,sloot ,yroeht eht ot stneduts secudortnI Less

More
Less