Ik-Pyo Kim | Daegu University (original) (raw)

Papers by Ik-Pyo Kim

Research paper thumbnail of Effects of phytohormones on regeneration from two explants in Lycopersicum esculentum

Two explants from Lycopersicum esculentum were cultured on MS medium supplemented with 6-BA,IAA a... more Two explants from Lycopersicum esculentum were cultured on MS medium supplemented with 6-BA,IAA and NAA of different density to induce regeneration plants. The results showed that the callus from leaf which has been induced on medium MS+6-BA2 mg/L(Unit is the same as follows)+NAA0.2 is not differentiated into bud by subculture, and on medium MS+6-BA2+IAA0.2 it can be differentiated into bud by subculture. It is favorable to induce callus of hypocotyl on medium MS+6-BA2.0+NAA0.2 and MS+6-BA2.0+IAA0.2, and bud may be directly induced with hypocotyl on medium MS+6-BA1.0.

Research paper thumbnail of Symmetric Bernoulli matrix and its Cholesky decomposition

Linear Algebra and its Applications, 2020

Abstract This study associates the symmetric Bernoulli matrix with various combinatorial matrices... more Abstract This study associates the symmetric Bernoulli matrix with various combinatorial matrices, such as Pascal, Vandermonde, and Stirling matrices of the first and second kind including Catalan numbers by way of dual matrices of the matrix. A recurrence relation related to the entries of the Cholesky factor of a symmetric positive definite matrix is presented, which sheds new light on examining positive definiteness and Cholesky's method of a symmetric matrix. This relation is applied to give a necessary and sufficient condition for the positive definiteness of a symmetric matrix, which leads to a slightly modified form of the outer-product formulation for Cholesky's method of a symmetric matrix.

Research paper thumbnail of Orientation of the Cross Product of 3-vectors

The College Mathematics Journal, 2019

(G1) The length of w is equal to the area of the parallelogram determined by u and v. (G2) w is p... more (G1) The length of w is equal to the area of the parallelogram determined by u and v. (G2) w is perpendicular to both u and v. (G3) The direction of w is described as follows: Place your right hand so that the index finger points in the direction of u and the middle finger points in the direction of v. Stretch your thumb so that it is perpendicular to both the index finger and the middle finger. Now your thumb will point in the direction of w.

Research paper thumbnail of Decompositions of a matrix by means of its dual matrices with applications

Linear Algebra and its Applications, 2018

Abstract We introduce the notion of dual matrices of an infinite matrix A, which are defined by t... more Abstract We introduce the notion of dual matrices of an infinite matrix A, which are defined by the dual sequences of the rows of A and naturally connected to the Pascal matrix P = [ ( i j ) ] ( i , j = 0 , 1 , 2 , … ) . We present the Cholesky decomposition of the symmetric Pascal matrix by means of its dual matrix. Decompositions of a Vandermonde matrix are used to obtain variants of the Lagrange interpolation polynomial of degree ≤n that passes through the n + 1 points ( i , q i ) for i = 0 , 1 , … , n .

Research paper thumbnail of (±1)-INVARIANT Sequences and Truncated Fibonacci Sequences of the Second Kind

Journal of the Korean Mathematical Society, 2005

Research paper thumbnail of (±1)-Invariant sequences and truncated Fibonacci sequences

Linear Algebra and its Applications, 2005

Research paper thumbnail of Pascal eigenspaces and invariant sequences of the first or second kind

Linear Algebra and its Applications, 2017

An infinite real sequence {a n } is called an invariant sequence of the first (resp., second) kin... more An infinite real sequence {a n } is called an invariant sequence of the first (resp., second) kind if a n = n k=0 n k (−1) k a k (resp., a n = ∞ k=n k n (−1) k a k). We review and investigate invariant sequences of the first and second kinds, and study their relationships using similarities of Pascal-type matrices and their eigenspaces.

Research paper thumbnail of 중학교 수학 수업에서 정수의 사칙계산의 원리에 따른 모델 선택에 관한 연구

The Mathematical Education, 2012

Research paper thumbnail of A Simple Proof of a Difference Sequence

Bulletin of the Korean Mathematical Society, 2005

Research paper thumbnail of Nearly tight sign-central matrices†

Linear and Multilinear Algebra, 2013

Research paper thumbnail of The number of zeros of a tight sign-central matrix

Linear Algebra and its Applications, 2005

A real matrix A is called sign-central if Ax = 0 has a nonzero nonnegative solution x for every m... more A real matrix A is called sign-central if Ax = 0 has a nonzero nonnegative solution x for every matrix A with the same sign pattern as A. A sign-central matrix A is called tight sign-central if the Hadamard(entrywise) product of any two columns of A contains a negative component. Hwang et al. [S.G. Hwang, I.P. Kim, S.J. Kim, X.D. Zhang, Tight sign-central matrices, Linear Algebra Appl. 371 (2003) 225-240] proved that, for a positive integer m, there exists an m × n (0, 1, −1) tight sign-central matrix A with no zero rows if and only if m + 1 n 2 m . They also determined the lower bound of the number of columns of a tight sign-central matrix with no zero rows in terms of the number of rows and the number of zero entries of the matrix along with the characterization of the equality case. For an m × n matrix A, the sparsity of A is the ratio σ (A)/mn where σ (A) denotes the number of zero entries of A.

Research paper thumbnail of Tight sign-central matrices

Linear Algebra and its Applications, 2003

A real matrix A is called sign-central if the convex hull of the columns of A contains the zero v... more A real matrix A is called sign-central if the convex hull of the columns of A contains the zero vector 0 for every matrix A with the same sign pattern as A. A sign-central matrix A is called a minimal sign-central matrix if the deletion of any of the columns of A breaks the signcentrality of A. A sign-central matrix A is called tight sign-central if the Hadamard (entrywise) product of any two columns of A contains a negative component. In this paper, we show that every tight sign-central matrix is minimal sign-central and characterize the tight sign-central matrices. We also determine the lower bound of the number of columns of a tight sign-central matrix in terms of the number of rows and the number of zero entries of the matrix.

Research paper thumbnail of LDU decomposition of an extension matrix of the Pascal matrix

Linear Algebra and its Applications, 2011

Research paper thumbnail of (±1)-Invariant sequences and truncated Fibonacci sequences

Linear Algebra and its Applications, 2005

Let P = i j , (i, j = 0, 1, 2, . . .) and D=diag((−1) 0 , (−1) 1 , (−1) 2 , . . . ). As a linear ... more Let P = i j , (i, j = 0, 1, 2, . . .) and D=diag((−1) 0 , (−1) 1 , (−1) 2 , . . . ). As a linear transformation of the infinite dimensional real vector space R ∞ = {(x 0 , x 1 , x 2 , . . .) T |x i ∈ R for all i}, PD has only two eigenvalues 1, −1. In this paper, we find some matrices associated with P whose columns form bases for the eigenspaces for PD. We also introduce truncated Fibonacci sequences and truncated Lucas sequences and show that these sequences span the eigenspaces of PD.

Research paper thumbnail of Effects of phytohormones on regeneration from two explants in Lycopersicum esculentum

Two explants from Lycopersicum esculentum were cultured on MS medium supplemented with 6-BA,IAA a... more Two explants from Lycopersicum esculentum were cultured on MS medium supplemented with 6-BA,IAA and NAA of different density to induce regeneration plants. The results showed that the callus from leaf which has been induced on medium MS+6-BA2 mg/L(Unit is the same as follows)+NAA0.2 is not differentiated into bud by subculture, and on medium MS+6-BA2+IAA0.2 it can be differentiated into bud by subculture. It is favorable to induce callus of hypocotyl on medium MS+6-BA2.0+NAA0.2 and MS+6-BA2.0+IAA0.2, and bud may be directly induced with hypocotyl on medium MS+6-BA1.0.

Research paper thumbnail of Symmetric Bernoulli matrix and its Cholesky decomposition

Linear Algebra and its Applications, 2020

Abstract This study associates the symmetric Bernoulli matrix with various combinatorial matrices... more Abstract This study associates the symmetric Bernoulli matrix with various combinatorial matrices, such as Pascal, Vandermonde, and Stirling matrices of the first and second kind including Catalan numbers by way of dual matrices of the matrix. A recurrence relation related to the entries of the Cholesky factor of a symmetric positive definite matrix is presented, which sheds new light on examining positive definiteness and Cholesky's method of a symmetric matrix. This relation is applied to give a necessary and sufficient condition for the positive definiteness of a symmetric matrix, which leads to a slightly modified form of the outer-product formulation for Cholesky's method of a symmetric matrix.

Research paper thumbnail of Orientation of the Cross Product of 3-vectors

The College Mathematics Journal, 2019

(G1) The length of w is equal to the area of the parallelogram determined by u and v. (G2) w is p... more (G1) The length of w is equal to the area of the parallelogram determined by u and v. (G2) w is perpendicular to both u and v. (G3) The direction of w is described as follows: Place your right hand so that the index finger points in the direction of u and the middle finger points in the direction of v. Stretch your thumb so that it is perpendicular to both the index finger and the middle finger. Now your thumb will point in the direction of w.

Research paper thumbnail of Decompositions of a matrix by means of its dual matrices with applications

Linear Algebra and its Applications, 2018

Abstract We introduce the notion of dual matrices of an infinite matrix A, which are defined by t... more Abstract We introduce the notion of dual matrices of an infinite matrix A, which are defined by the dual sequences of the rows of A and naturally connected to the Pascal matrix P = [ ( i j ) ] ( i , j = 0 , 1 , 2 , … ) . We present the Cholesky decomposition of the symmetric Pascal matrix by means of its dual matrix. Decompositions of a Vandermonde matrix are used to obtain variants of the Lagrange interpolation polynomial of degree ≤n that passes through the n + 1 points ( i , q i ) for i = 0 , 1 , … , n .

Research paper thumbnail of (±1)-INVARIANT Sequences and Truncated Fibonacci Sequences of the Second Kind

Journal of the Korean Mathematical Society, 2005

Research paper thumbnail of (±1)-Invariant sequences and truncated Fibonacci sequences

Linear Algebra and its Applications, 2005

Research paper thumbnail of Pascal eigenspaces and invariant sequences of the first or second kind

Linear Algebra and its Applications, 2017

An infinite real sequence {a n } is called an invariant sequence of the first (resp., second) kin... more An infinite real sequence {a n } is called an invariant sequence of the first (resp., second) kind if a n = n k=0 n k (−1) k a k (resp., a n = ∞ k=n k n (−1) k a k). We review and investigate invariant sequences of the first and second kinds, and study their relationships using similarities of Pascal-type matrices and their eigenspaces.

Research paper thumbnail of 중학교 수학 수업에서 정수의 사칙계산의 원리에 따른 모델 선택에 관한 연구

The Mathematical Education, 2012

Research paper thumbnail of A Simple Proof of a Difference Sequence

Bulletin of the Korean Mathematical Society, 2005

Research paper thumbnail of Nearly tight sign-central matrices†

Linear and Multilinear Algebra, 2013

Research paper thumbnail of The number of zeros of a tight sign-central matrix

Linear Algebra and its Applications, 2005

A real matrix A is called sign-central if Ax = 0 has a nonzero nonnegative solution x for every m... more A real matrix A is called sign-central if Ax = 0 has a nonzero nonnegative solution x for every matrix A with the same sign pattern as A. A sign-central matrix A is called tight sign-central if the Hadamard(entrywise) product of any two columns of A contains a negative component. Hwang et al. [S.G. Hwang, I.P. Kim, S.J. Kim, X.D. Zhang, Tight sign-central matrices, Linear Algebra Appl. 371 (2003) 225-240] proved that, for a positive integer m, there exists an m × n (0, 1, −1) tight sign-central matrix A with no zero rows if and only if m + 1 n 2 m . They also determined the lower bound of the number of columns of a tight sign-central matrix with no zero rows in terms of the number of rows and the number of zero entries of the matrix along with the characterization of the equality case. For an m × n matrix A, the sparsity of A is the ratio σ (A)/mn where σ (A) denotes the number of zero entries of A.

Research paper thumbnail of Tight sign-central matrices

Linear Algebra and its Applications, 2003

A real matrix A is called sign-central if the convex hull of the columns of A contains the zero v... more A real matrix A is called sign-central if the convex hull of the columns of A contains the zero vector 0 for every matrix A with the same sign pattern as A. A sign-central matrix A is called a minimal sign-central matrix if the deletion of any of the columns of A breaks the signcentrality of A. A sign-central matrix A is called tight sign-central if the Hadamard (entrywise) product of any two columns of A contains a negative component. In this paper, we show that every tight sign-central matrix is minimal sign-central and characterize the tight sign-central matrices. We also determine the lower bound of the number of columns of a tight sign-central matrix in terms of the number of rows and the number of zero entries of the matrix.

Research paper thumbnail of LDU decomposition of an extension matrix of the Pascal matrix

Linear Algebra and its Applications, 2011

Research paper thumbnail of (±1)-Invariant sequences and truncated Fibonacci sequences

Linear Algebra and its Applications, 2005

Let P = i j , (i, j = 0, 1, 2, . . .) and D=diag((−1) 0 , (−1) 1 , (−1) 2 , . . . ). As a linear ... more Let P = i j , (i, j = 0, 1, 2, . . .) and D=diag((−1) 0 , (−1) 1 , (−1) 2 , . . . ). As a linear transformation of the infinite dimensional real vector space R ∞ = {(x 0 , x 1 , x 2 , . . .) T |x i ∈ R for all i}, PD has only two eigenvalues 1, −1. In this paper, we find some matrices associated with P whose columns form bases for the eigenspaces for PD. We also introduce truncated Fibonacci sequences and truncated Lucas sequences and show that these sequences span the eigenspaces of PD.