2023-12-09T02:57:48+03:00[Europe/Moscow] en true <p>How are determinants affected by replacement, interchange, and scaling</p>, <p>What is the determinant of triangular matrix?</p>, <p>When is the det(A) = 0?</p>, <p>What is the det(AB)? What is the det(A^T) ( N x N matrices)</p>, <p>What is co factor expansion?</p>, <p>Form of an eigenvector and what is an eigenvalue</p>, <p>Definition of an eigenspace</p>, <p>When is lambda an eigenvalue of a matrix A? (N x N)</p>, <p>How to solve for the eigenspace using Nul</p>, <p>What is algebraic and geometric multiplicity</p>, <p>What is the trace of a matrix A w/o knowing the eigenvalues</p>, <p>What is the trace and a det of a matrix A with known eigenvalues</p>, <p>What makes a square matrix diagonalizable</p>, <p>What is P and D comprised of when diagonalizing a matrix</p>, <p>What is an eigenbasis</p>, <p>Finding the diagonal matrix using change a bases matrices</p>, <p>How to calculate the power of a diagonal matrix.</p>, <p>how to find exp(At) of a matrix A</p>, <p>What is the orthogonal projection v onto the line spanned by w (eqn and definition</p>, <p>What is the orthogonal projection v onto the line spanned by w for matrix multiplication?</p>, <p>How to project a vector onto a subspace?</p>, <p>What is the orthogonal projection matrix?</p>, <p>when is x^ a LSQ?</p>, <p>what is the proj(b) onto the col(A)?</p>, <p>What is the Gram-Schmidt algorithm? </p>, <p>What is QR decomposition?</p>, <p>What does a matrix A have an orthonormal set of eigenvectors?</p>, <p>If A is a symmetrix N x N matrix, what makes up A? </p>, <p>What is SVD? Explain the parts that comprise SVD.</p>, <p>What is the algorithm for SVD?</p>, <p>If U,V,Sigma are the SVD of a matrix A, what bases do they comprise (4 bases)</p>, <p>What is A for an SVD matrix?</p>, <p>What is a compact singular value decomp?</p>, <p>What is the pseudoinverse?</p>, <p>What is the LSQ soln of Ax = b with pseudoinverse?</p>, <p>What is the column average of X? When is X centered and what is the covariance matrix Cov(X) of X? (PCA)</p>, <p>What is the algorithm for PCA</p>, <p>What are the properties of eigenvalues of a markov matrix?</p>, <p>What is the unique soln to the diff eqn with initial conditions?</p> flashcards

Math 257

Weeks 8-14

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  • How are determinants affected by replacement, interchange, and scaling

  • What is the determinant of triangular matrix?

  • When is the det(A) = 0?

  • What is the det(AB)? What is the det(A^T) ( N x N matrices)

  • What is co factor expansion?

  • Form of an eigenvector and what is an eigenvalue

  • Definition of an eigenspace

  • When is lambda an eigenvalue of a matrix A? (N x N)

  • How to solve for the eigenspace using Nul

  • What is algebraic and geometric multiplicity

  • What is the trace of a matrix A w/o knowing the eigenvalues

  • What is the trace and a det of a matrix A with known eigenvalues

  • What makes a square matrix diagonalizable

  • What is P and D comprised of when diagonalizing a matrix

  • What is an eigenbasis

  • Finding the diagonal matrix using change a bases matrices

  • How to calculate the power of a diagonal matrix.

  • how to find exp(At) of a matrix A

  • What is the orthogonal projection v onto the line spanned by w (eqn and definition

  • What is the orthogonal projection v onto the line spanned by w for matrix multiplication?

  • How to project a vector onto a subspace?

  • What is the orthogonal projection matrix?

  • when is x^ a LSQ?

  • what is the proj(b) onto the col(A)?

  • What is the Gram-Schmidt algorithm?

  • What is QR decomposition?

  • What does a matrix A have an orthonormal set of eigenvectors?

  • If A is a symmetrix N x N matrix, what makes up A?

  • What is SVD? Explain the parts that comprise SVD.

  • What is the algorithm for SVD?

  • If U,V,Sigma are the SVD of a matrix A, what bases do they comprise (4 bases)

  • What is A for an SVD matrix?

  • What is a compact singular value decomp?

  • What is the pseudoinverse?

  • What is the LSQ soln of Ax = b with pseudoinverse?

  • What is the column average of X? When is X centered and what is the covariance matrix Cov(X) of X? (PCA)

  • What is the algorithm for PCA

  • What are the properties of eigenvalues of a markov matrix?

  • What is the unique soln to the diff eqn with initial conditions?