{"product_id":"9781605010823","title":"Linear Algebra Study Guide","description":"\u003cp\u003eBoost Your grades with this illustrated Study Guide. You will use it from college all the way to graduate school and beyond.\u003c\/p\u003e  \u003cp\u003e\u003cb\u003eFeatures\u003c\/b\u003e\u003c\/p\u003e  \u003cul\u003e   \u003cli\u003eClear and concise explanations \u003c\/li\u003e   \u003cli\u003eDifficult concepts are explained in simple terms \u003c\/li\u003e   \u003cli\u003eIllustrated with graphs and diagrams \u003c\/li\u003e  \u003c\/ul\u003e  \u003cp\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003c\/p\u003e  \u003cp\u003e\u003cb\u003eI. Linear equations\u003c\/b\u003e\u003c\/p\u003e  \u003cul\u003e   \u003cli\u003eSystem of linear equations \u003c\/li\u003e   \u003cli\u003eDeterminant    \u003cul\u003e      \u003cli\u003eMinor \u003c\/li\u003e     \u003cli\u003eCauchy-Binet formula \u003c\/li\u003e    \u003c\/ul\u003e   \u003c\/li\u003e   \u003cli\u003eCramer's rule \u003c\/li\u003e   \u003cli\u003eGaussian elimination \u003c\/li\u003e   \u003cli\u003eGauss-Jordan elimination \u003c\/li\u003e   \u003cli\u003eStrassen algorithm \u003c\/li\u003e  \u003c\/ul\u003e  \u003cp\u003e\u003cb\u003eII. Matrices\u003c\/b\u003e\u003c\/p\u003e  \u003cul\u003e   \u003cli\u003eMatrix addition \u003c\/li\u003e   \u003cli\u003eMatrix multiplication \u003c\/li\u003e   \u003cli\u003eBasis transformation matrix \u003c\/li\u003e   \u003cli\u003eCharacteristic polynomial, Characteristic Equation \u003c\/li\u003e   \u003cli\u003eTrace \u003c\/li\u003e   \u003cli\u003eEigenvalue, eigenvector and eigenspace    \u003cul\u003e      \u003cli\u003eCayley-Hamilton theorem \u003c\/li\u003e     \u003cli\u003eSpread of a matrix \u003c\/li\u003e     \u003cli\u003eSymbolic Computation of Matrix Eigenvalues \u003c\/li\u003e    \u003c\/ul\u003e   \u003c\/li\u003e   \u003cli\u003eJordan normal form \u003c\/li\u003e   \u003cli\u003eRank \u003c\/li\u003e   \u003cli\u003eMatrix inversion,    \u003cul\u003e      \u003cli\u003ePseudoinverse \u003c\/li\u003e    \u003c\/ul\u003e   \u003c\/li\u003e   \u003cli\u003eAdjugate \u003c\/li\u003e   \u003cli\u003eTranspose    \u003cul\u003e      \u003cli\u003eDot product \u003c\/li\u003e     \u003cli\u003eSymmetric matrix \u003c\/li\u003e     \u003cli\u003eMatrix congruence      \u003cul\u003e         \u003cli\u003eCongruence relation \u003c\/li\u003e      \u003c\/ul\u003e     \u003c\/li\u003e     \u003cli\u003eOrthogonal matrix \u003c\/li\u003e     \u003cli\u003eSkew-symmetric matrix \u003c\/li\u003e     \u003cli\u003eConjugate transpose      \u003cul\u003e         \u003cli\u003eUnitary matrix \u003c\/li\u003e       \u003cli\u003eHermitian matrix, Antihermitian \u003c\/li\u003e      \u003c\/ul\u003e     \u003c\/li\u003e    \u003c\/ul\u003e   \u003c\/li\u003e   \u003cli\u003ePositive definite: matrix, function, bilinear form \u003c\/li\u003e   \u003cli\u003eIdentity matrix \u003c\/li\u003e   \u003cli\u003ePfaffian \u003c\/li\u003e   \u003cli\u003eProjection \u003c\/li\u003e   \u003cli\u003eDiagonal matrix, main diagonal    \u003cul\u003e      \u003cli\u003eDiagonalizable matrix \u003c\/li\u003e    \u003c\/ul\u003e   \u003c\/li\u003e   \u003cli\u003eSimilar matrix \u003c\/li\u003e   \u003cli\u003eTridiagonal matrix \u003c\/li\u003e   \u003cli\u003eHessenberg matrix \u003c\/li\u003e   \u003cli\u003eTriangular matrix \u003c\/li\u003e   \u003cli\u003eSpectral theorem \u003c\/li\u003e   \u003cli\u003eStochastic matrix \u003c\/li\u003e   \u003cli\u003eToeplitz matrix    \u003cul\u003e      \u003cli\u003eCirculant matrix \u003c\/li\u003e    \u003c\/ul\u003e   \u003c\/li\u003e   \u003cli\u003eHankel matrix \u003c\/li\u003e   \u003cli\u003eVandermonde matrix \u003c\/li\u003e   \u003cli\u003eBlock matrix \u003c\/li\u003e   \u003cli\u003e(0,1)-matrix \u003c\/li\u003e   \u003cli\u003eNormal Matrix \u003c\/li\u003e   \u003cli\u003eSparse matrix \u003c\/li\u003e   \u003cli\u003eWoodbury matrix identity \u003c\/li\u003e   \u003cli\u003ePerron-Frobenius theorem \u003c\/li\u003e   \u003cli\u003eList of Matrices \u003c\/li\u003e  \u003c\/ul\u003e  \u003cp\u003e\u003cb\u003eIII. Matrix decompositions\u003c\/b\u003e\u003c\/p\u003e  \u003cul\u003e   \u003cli\u003eBlock LU Decomposition \u003c\/li\u003e   \u003cli\u003eCholesky decomposition \u003c\/li\u003e   \u003cli\u003eLU decomposition \u003c\/li\u003e   \u003cli\u003eQR decomposition \u003c\/li\u003e   \u003cli\u003eSpectral theorem \u003c\/li\u003e   \u003cli\u003eSingular value decomposition \u003c\/li\u003e   \u003cli\u003eSchur decomposition    \u003cul\u003e      \u003cli\u003eSchur complement \u003c\/li\u003e    \u003c\/ul\u003e   \u003c\/li\u003e  \u003c\/ul\u003e  \u003cp\u003e\u003cb\u003eIV. Computations\u003c\/b\u003e\u003c\/p\u003e  \u003cul\u003e   \u003cli\u003eTransformation Matrix \u003c\/li\u003e   \u003cli\u003eHouseholder transformation \u003c\/li\u003e   \u003cli\u003eLeast squares, linear least squares \u003c\/li\u003e   \u003cli\u003eGram-Schmidt process \u003c\/li\u003e  \u003c\/ul\u003e  \u003cp\u003e\u003cb\u003eV. Vectors\u003c\/b\u003e\u003c\/p\u003e  \u003cul\u003e   \u003cli\u003eUnit Vector \u003c\/li\u003e   \u003cli\u003ePseudovector \u003c\/li\u003e   \u003cli\u003eNormal Vector \u003c\/li\u003e   \u003cli\u003eTangential and Normal Components \u003c\/li\u003e   \u003cli\u003eScalar multiplication \u003c\/li\u003e   \u003cli\u003eLinear combination \u003c\/li\u003e   \u003cli\u003eLinear span \u003c\/li\u003e   \u003cli\u003eLinear independence \u003c\/li\u003e   \u003cli\u003eBasis \u003c\/li\u003e  \u003c\/ul\u003e  \u003cp\u003e\u003cb\u003eVI. Vector spaces\u003c\/b\u003e\u003c\/p\u003e  \u003cul\u003e   \u003cli\u003eBasis=Hamel basis \u003c\/li\u003e   \u003cli\u003eDimension theorem for vector spaces=Hamel dimension \u003c\/li\u003e   \u003cli\u003eExamples of vector spaces \u003c\/li\u003e   \u003cli\u003eLinear map    \u003cul\u003e      \u003cli\u003eGalilean transformation, Lorentz transformation \u003c\/li\u003e    \u003c\/ul\u003e   \u003c\/li\u003e   \u003cli\u003eRow and Column space \u003c\/li\u003e   \u003cli\u003eNull space \u003c\/li\u003e   \u003cli\u003eRank-nullity theorem \u003c\/li\u003e   \u003cli\u003eDual space    \u003cul\u003e      \u003cli\u003eLinear function \u003c\/li\u003e     \u003cli\u003eLinear functional \u003c\/li\u003e    \u003c\/ul\u003e   \u003c\/li\u003e   \u003cli\u003eOrthogonality \u003c\/li\u003e   \u003cli\u003eOrthogonal complement \u003c\/li\u003e   \u003cli\u003eOrthogonal projection \u003c\/li\u003e  \u003c\/ul\u003e  \u003cp\u003e...\u003c\/p\u003e                    ","brand":"MobileReference","offers":[{"title":"Default Title","offer_id":47147876581616,"sku":"9781605010823","price":9.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0737\/7593\/9824\/files\/9781605010823_p0.jpg?v=1763827145","url":"https:\/\/shop-qa.barnesandnoble.com\/products\/9781605010823","provider":"Barnes \u0026 Noble (DEV)","version":"1.0","type":"link"}