Introduction to linear Algebra

By C. Tay, H. Sakidin, I. W. Jamaludin, Norazlina Abdul Razak, N. Apandi. 2010

1,963 citations recorded by the source corpus.

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Pure Mathematics

Citations in the corpus

Mass-Editing Memory in a Transformer (2022, methodology): “7 can be optimized by solving the normal equation (Strang, 1993, Chapter 4): Suppose that pre-training sets a transformer MLP’s weights to the optimal solution W 0 as defined in Eqn.”
Functional Mechanism: Regression Analysis under Differential Privacy (2012, background): “In addition, ¯ f D ( ω ) is unbounded if and only if M ∗ + λI is not positive deﬁnite, which holds if and only if at least one eigenvalue of M ∗ + λI is not positive [28].”
Julia: A Fresh Approach to Numerical Computing (2014, methodology): “For symmetric tridiagonals the usual three-term recurrence formula [31] is used.”
Multiple antenna spectrum sensing in cognitive radios (2010, methodology): “We can easily show that det(R) = (σ(2) s∥h∥(2) + σ(2) n)(σ 2 n) (M−1) and also by using the matrix inversion lemma [22], we obtain:”
Compositional Matrix-Space Models of Language (2010, background): “For a more thorough treatise we refer the reader to a linear algebra textbook (such as Strang (1993)).”
EigenTHREADER: analogous protein fold recognition by efficient contact map threading (2017, methodology): “The Al-Eigen method uses eigendecomposition of symmetric matrices (Strang, 2016) and the Needleman-Wunsch alignment algorithm (Needleman and Wunsch, 1970) to achieve high quality contact map alignments in polynomial time.”
Principal Component Analysis (2018, background): “, Strang [1993]), for a more complete description of vector spaces and their properties.”
Fixed-domain asymptotic properties of tapered maximum likelihood estimators (2009, background): “, Pissanetzky (1984), Gilbert, Moler and Schreiber (1992) and Davis (2006)].”
Application of Convex Relaxation to Array Synthesis Problems (2014, background): “The best one, in the least two norm sense, can be obtained via a eigenvalue decomposition [15] as follows: X∗1 = σ1u1u1 T , (10) where σ1 is the largest eigenvalue of X ∗ and u1 is the corresponding eigen vector.”
The Design of Approximation Algorithms (2011, background): “Strang [273, 274] provides introductions to linear algebra that are useful in the context of our discussion of semidefinite programming and various operations on vectors and matrices.”
Principles of Uncertainty (2011, background): “We now do something more ambitious, and characterize orthogonal matrices among all transformations: Mirsky (1990), Theorem 8.”
Dive into Deep Learning (2020, background): “If you are eager to learn more about linear algebra, you may refer to either the online appendix on linear algebraic operations40 or other excellent resources (Strang, 1993; Kolter, 2008; Petersen et al., 2008).”
Non-Hermitian systems and topology: A transfer-matrix perspective (2018, methodology): “In this degenerate sector, we set v = (v, ṽ) and w = (w, w̃) to write the SVD of J in this subspace as v 1 2 w.”
Cauchy-Binet for Pseudo-Determinants (2013, neutral): “The pseudo-determinant of a square matrix A is defined as the product of the nonzero eigenvalues of A with the convention that the pseudo-determinant of the 0 matrix is defined to be zero.”