**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**3

# Determinant Related Publications

##### 3 A Time-Reducible Approach to Compute Determinant |I-X|

**Authors:**
Wang Xingbo

**Abstract:**

*X*| is primary and fundamental because it can help to compute many other determinants. This article puts forward a time-reducible approach to compute determinant |I-

*X*|. The approach is derived from the Newton’s identity and its time complexity is no more than that to compute the eigenvalues of the square matrix

*X*. Mathematical deductions and numerical example are presented in detail for the approach. By comparison with classical approaches the new approach is proved to be superior to the classical ones and it can naturally reduce the computational time with the improvement of efficiency to compute eigenvalues of the square matrix.

**Keywords:**
Computation,
Algorithm,
Determinant,
eigenvalue,
time complexity

##### 2 The Determinants of Corporate Cash Holdings in Nigeria: Evidence from General Method of Moments (GMM)

**Authors:**
Sunday E. Ogundipe,
Rafiu O. Salawu,
Lawrencia O. Ogundipe

**Abstract:**

The study examines the determinants of corporate cash holding of non-financial quoted firms in Nigeria using a sample of fifty four non-financial quoted firms listed on the Nigeria Stock Exchange for the period 1995-2009. Data were sourced from the Annual reports of the sampled firms and analyzed using Generalized Method of Moments(GMM). The study finds evidence supportive of a target adjustment model and that firms can not instantaneously adjust towards the target cash level owing to the fact that adjustment cost being costly,. Also, the result shows significant negative relationship between cash holdings and firm size, net working capital, return on asset and bank relationship and positive relationship with growth opportunities, leverage, inventories, account receivables and financial distress. Furthermore, there is no significant relationship between cash holdings and cash flow. In Nigerian setting, most of the variables that are relevant for explaining cash holdings in the Developed countries are found by this study to be relevant also in Nigeria.

**Keywords:**
Determinant,
Adjustment Model,
Cash holding,
Generalized Method of Moments(GMM)

##### 1 New Scheme in Determining nth Order Diagrams for Cross Multiplication Method via Combinatorial Approach

**Authors:**
Sharmila Karim,
Haslinda Ibrahim,
Zurni Omar

**Abstract:**

In this paper, a new recursive strategy is proposed for determining $\frac{(n-1)!}{2}$ of $n$th order diagrams. The generalization of $n$th diagram for cross multiplication method were proposed by Pavlovic and Bankier but the specific rule of determining $\frac{(n-1)!}{2}$ of the $n$th order diagrams for square matrix is yet to be discovered. Thus using combinatorial approach, $\frac{(n-1)!}{2}$ of the $n$th order diagrams will be presented as $\frac{(n-1)!}{2}$ starter sets. These starter sets will be generated based on exchanging one element. The advantages of this new strategy are the discarding process was eliminated and the sign of starter set is alternated to each others.

**Keywords:**
Determinant,
permutation,
starter sets,
exchanging one element