Boost Your grades with this illustrated Study Guide. You will use it from college all the way to graduate school and beyond. Features Clear and concise explanations Difficult concepts are explained in simple terms Illustrated with graphs and diagrams Table of Contents I. Linear equations System of linear equations Determinant Minor Cauchy-Binet formula Cramer's rule Gaussian elimination Gauss-Jordan elimination Strassen algorithm II. Matrices Matrix addition Matrix multiplication Basis transformation matrix Characteristic polynomial, Characteristic Equation Trace Eigenvalue, eigenvector and eigenspace Cayley-Hamilton theorem Spread of a matrix Symbolic Computation of Matrix Eigenvalues Jordan normal form Rank Matrix inversion, Pseudoinverse Adjugate Transpose Dot product Symmetric matrix Matrix congruence Congruence relation Orthogonal matrix Skew-symmetric matrix Conjugate transpose Unitary matrix Hermitian matrix, Antihermitian Positive definite: matrix, function, bilinear form Identity matrix Pfaffian Projection Diagonal matrix, main diagonal Diagonalizable matrix Similar matrix Tridiagonal matrix Hessenberg matrix Triangular matrix Spectral theorem Stochastic matrix Toeplitz matrix Circulant matrix Hankel matrix Vandermonde matrix Block matrix (0,1)-matrix Normal Matrix Sparse matrix Woodbury matrix identity Perron-Frobenius theorem List of Matrices III. Matrix decompositions Block LU Decomposition Cholesky decomposition LU decomposition QR decomposition Spectral theorem Singular value decomposition Schur decomposition Schur complement IV. Computations Transformation Matrix Householder transformation Least squares, linear least squares Gram-Schmidt process V. Vectors Unit Vector Pseudovector Normal Vector Tangential and Normal Components Scalar multiplication Linear combination Linear span Linear independence Basis VI. Vector spaces Basis=Hamel basis Dimension theorem for vector spaces=Hamel dimension Examples of vector spaces Linear map Galilean transformation, Lorentz transformation Row and Column space Null space Rank-nullity theorem Dual space Linear function Linear functional Orthogonality Orthogonal complement Orthogonal projection ...