• Journal of Educational Research in Mathematics
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• v.25 no.2
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• pp.177-188
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• 2015

In this paper, I investigated the historical development process for the product of two vectors in the plane and space, and draw implications for educational guidance to internal and external product of vectors based on it. The results of the historical analysis show that efforts to define the product of the two line segments having different direction in the plane justified the rules of complex algebraic calculations with its length of the product of their lengths and its direction of the sum of their directions. Also, the efforts to define the product of the two line segments having different direction in three dimensional space led to the introduction of quaternion. In addition, It is founded that the inner product and outer product of vectors was derived from the real part and vector part of multiplication of two quaternions. Based on these results, I claimed that we should review the current deployment method of making inner product and outer product as multiplications that are not related to each other, and suggested one approach for connecting the inner and outer product.

• The Pure and Applied Mathematics
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• v.29 no.1
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• pp.103-112
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• 2022

A definition of fractional vector cross product of two vectors in Euclidean 3-space is presented. The formulas for Euclidean norm of the fractional vector cross product of two vectors, and for fractional triple vector cross product are obtained.

• Proceedings of the Optical Society of Korea Conference
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• 1990.02a
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• pp.102-111
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• 1990

In this thesis, an optical bidirectional inner-product associative memory model using liquid crystal television is proposed and analyzed theoretically and realized experimentally. The LCTV is used as a SLM(spatial light modulator), which is more practical than conventional SLMs, to produce image vector in terms of computer and CCD camera. Memory and input vectors are recorded into each LCTV through the video input connectors of it by using the image board. Two multi-focus hololenses are constructed in order to perform optical inner-product process. In forward process, the analog values of inner-products are measured by photodetectors and are converted to digital values which are enable to control the weighting values of the stored vectors by changing the gray levels of the pixels of the LCTV. In backward process, changed stored vectors are used to produce output image vector which is used again for input vector after thresholding. After some iterations, one of the stored vectors is retrieved which is most similar to input vector in other words, has the nearest hamming distance. The experimental results show that the proposed inner-product associative memory model can be realized optically and coincide well with the computer simulation.

• Proceedings of the IEEK Conference
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• 2004.08c
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• pp.503-508
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• 2004

This paper proposes an efficient computation method for fixed and mixed polarity Reed -Muller function vector over Galois field GF(p). Function vectors of fixed polarity Heed Muller function with single variable can be generated by proposed method. The n-variable function vectors can be calculated by means of the Kronecker product of a single variable function vector corresponding to each variable. Thus, all fixed and mixed polarity Reed-Muller function vectors are calculated directly without using a polarity function vector table or polarity coefficient matrix.

• Journal of the Korean Statistical Society
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• v.22 no.2
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• pp.339-345
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• 1993

It is well known that distribution of functions of eigen values and vectors of a certain matrix plays an important role in multivariate analysis. This paper deals with the transformation of a correlation-type random matrix to its eigen values and vectors. Properties of the transformation are also considered. The results obtained are applied to express the joint distribution of eigen values and vectors of the correlation matrix when sample is taken from a m-variate spherical distribution.

• Journal of information and communication convergence engineering
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• v.5 no.1
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• pp.12-16
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• 2007

In this paper, a new method is proposed for tracking the direction-of-arrival (DOA) of the wideband moving source incident on uniform linear array sensors. DOA is estimated by focusing transformation matrices. To update focusing matrices along with new data snap shots, we use the FAST (Fast Approximate Subspace Tracking) method. Present focusing matrices are constructed by previous signal and its orthogonal basis vectors as well as present signal and its orthogonal basis vectors, which are the left and right singular vectors of the inner product of two approximated matrices. Simulation results are shown to illustrate the performance of the proposed method.

• Journal of the Chungcheong Mathematical Society
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• v.19 no.3
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• pp.291-297
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• 2006

We find unit Killing vectors and homogeneous geodesics on the Lie group with Lie algebra $\mathbf{a}{\oplus}_p\mathbf{r}$, where $\mathbf{a}$ and $\mathbf{r}$ are abelian Lie algebra of dimension n and 1, respectively.

• Korean Journal of Mathematics
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• v.8 no.2
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• pp.155-162
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• 2000

For a sequence $\{{\eta}_m\}_m$ of unit vectors in $\mathbb{C}^n$, we consider the associated linear functional ${\omega}$ on the Cuntz algebra $\mathcal{O}_n$. We show that the restriction ${\omega}{\mid}_{UHF_n}$ is the product pure state of a subalgebra $UHF_n$ of $\mathcal{O}_n$ such that ${\omega}{\mid}_{UHF_n}={\otimes}{\omega}_m$ with ${\omega}_m({\cdot})$ < ${\cdot}{\eta}_m,{\eta}_m$ >. We study product pure states of UHF and obtain a concrete description of them in terms of unit vectors. We also study states of $UHF_n$ which is the restriction of the linear functionals on $O_n$ associated to a fixed unit vector in $\mathbb{C}^n$.

• Journal of the Korean Mathematical Society
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• v.40 no.1
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• pp.1-28
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• 2003

The Iwahori-Hecke algebra $H_{k}$ ( $q^2$) of type A acts on the k-fold tensor product space of the natural representation of the quantum superalgebra (equation omitted)$_{q}$(gl(m, n)). We show the Hecke algebra $H_{k}$ ( $q^2$) and the quantum superalgebra (equation omitted)$_{q}$(gl(m n)) have commuting actions on the tensor product space, and determine the centralizer of each other. Using this result together with Gyoja's q-analogue of the Young symmetrizers, we construct highest weight vectors of irreducible summands of the tensor product space.

• Korean Journal of Remote Sensing
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• v.24 no.6
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• pp.641-644
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• 2008

In order to improve a camera rotation calculation based on the bundle adjustment in Chon's camera motion (Chon and Shankar, 2007, 2008), this paper introduces a method calculating the camera rotation. It estimates a unit vector in the optical axis of a camera through the angles between the optical axis and vectors passing a camera position and ground control points (GCP). The camera position is estimated by using the inner product method proposed by Chon. The horizontal and vertical unit vectors of the camera are determined by using Yakimovsky and Cunningham's camera model (CAHV) (1978).