Linear Algebra: A Modern IntroductionIn this innovative new Linear Algebra text, award-winning educator David Poole covers vectors and vector geometry first to enable students to visualize the mathematics while they are doing matrix operations. Rather than merely doing the calculations with no understanding of the mathematics, students will be able to visualize and understand the meaning of the calculations. By seeing the mathematics and understanding the underlying geometry, students will develop mathematical maturity and learn to think abstractly. |
Contents
CHAPTER | 10 |
The Cross Product | 46 |
Systems of Linear Equations | 57 |
Copyright | |
15 other sections not shown
Common terms and phrases
A₁ A₂ approximation augmented matrix c₁ c₂ calculations Chapter check digit code vector col(A complex numbers components compute coordinate vector corresponding defined definition denoted determine diagonal diagonalizable direction vector dot product e₁ eigenvalues eigenvectors elementary row operations entries equivalent error Exercise formula Gauss-Jordan elimination Gauss-Seidel method geometric given gives Gram-Schmidt Process graph Hence inequality inner product integer invertible iterates least squares linear algebra linear combination linear equations linear system linear transformation linearly independent mathematics method nonzero norm nxn matrix obtain orthogonal matrix orthonormal P₁ P₂ parity check plane Problem projw(v proof properties Prove rank(A real numbers reduced row echelon result row echelon form scalar multiplication Section set of vectors singular values solve span subspace symmetric system of linear Theorem tion u₁ unit vector V₁ V₂ variables vector space x₁