Matrix
Multiplication
Management Team
1. Reem Mohamed Abdelwahab
2. Aya Hesham Abdelwahab
3. Nourhan Abdelmohsen Abdelrazek
4. Assem Mohamed Ellithy
5. Ahmed Tarek hussien
6. Aly Mohamed Abdelsadek
What is matrix multiplication?
• Matrix multiplication is an operation performed on two matrices to produce a
new matrix. It is a fundamental operation in linear algebra and has various
applications in mathematics, physics, computer graphics, and data analysis
• Matrix multiplication is a fundamental operation that allows engineers to
manipulate and analyze data efficiently.
Matrix importance in real life
• representing data
Matrices can effectively represent and organize complex data structures, They provide a compact and
organized way to handle large datasets
• transforming data
Matrix multiplication is used to transform data from one form to another. it can be used to rotate, scale, or
translate vectors, which is essential in image processing and computer graphics.
• solving systems of equations
Matrix multiplication is a key component of solving systems of linear equations, which arise in various
applications, such as engineering design, economics modeling, and scientific simulations. By representing the
equations as matrices, matrix multiplication can efficiently solve these systems and provide valuable insights.
Matrix importance in real life
• representing relationships
Matrices can represent relationships between entities, such as the connections between nodes in a network or
the correlations between variables in a dataset.
• efficient calculations
Matrix multiplication is computationally efficient, especially for large matrices, making it suitable for highperformance computing applications. Specialized algorithms and hardware implementations have been
developed to accelerate matrix multiplication,
Uses of matrix multiplication in
finance
• Combine and summarize financial data
a multiplication matrix could be used to combine data from a general ledger, a sales ledger, and a
purchase ledger to create a consolidated financial statement.
• Allocate costs and expenses
a multiplication matrix could be used to allocate overhead costs to different departments based on
their share of direct labor costs.
Uses of matrix multiplication in
finance
• Solve complex accounting problems
• a multiplication matrix could be used to calculate the economic order quantity (EOQ) for a
product.
• Analyze financial data
• a multiplication matrix could be used to analyze sales data to identify which products are selling
well and which products are not.
How do the CIB use multiplication in
matrices?
• CIB uses multiplication in matrices to consolidate the financial statements
of its subsidiaries this is a very difficult process but Multiplication matrices
can be used to simplify this process by automating the calculations and
ensuring that the data is accurate and consistent.
• CIB uses multiplication in matrices to optimize investment portfolio Matrix
multiplication can be used to find the optimal allocation of assets in a
portfolio, given certain risk and return
CIB uses multiplication matrices to calculate depreciation for a variety of asset and
using a variety of methods, such as straight-line depreciation, declining-balance
depreciation, and sum-of-the-years'-digits depreciation.
Matrix multiplication in Engineering
Matrix multiplication is a fundamental operation that allows
engineers to manipulate and analyze data efficiently.
Understanding the principles of matrix multiplication is key
to solve complex engineering problems.
Benefits of Matrix Multiplication in
Engineering
1-Efficiency
Matrix multiplication allows engineers to perform calculations on large sets of
data rapidly, contributing to faster analyses and simulations in various
engineering fields.
2-Accuracy
By utilizing matrices, engineers can represent complex systems accurately,
ensuring precise calculations and reliable predictions for real-world applications.
Applications of matrix multiplication in
engineering
• Power Systems Analysis in (Electrical engineering)
Matrix Multiplication is used to solve power flow equations in electrical
networks, enabling engineers to optimize the stability and efficiency of power
systems.
• vibration analysis in ( Mechanical engineering)
Matrices are used to model the dynamic behavior of mechanical systems
under vibration.
Multiplying matrices helps analyze natural frequencies and modes
of
vibration.
How do civil engineers use matrix multiplication?
• Structural Analysis : Matrix multiplication is used to analyze complex structural
systems such as bridges and buildings ensuring their safety and stability.
• Traffic Flow Simulation : by representing traffic patterns and road networks
with matrices, civil engineers can simulate and optimize traffic flow for efficient
transportation planning and design.
CONCLUSION
Matrix multiplication is an indispensable tool in both finance and engineering.
provides engineers and financial experts with powerful tools to model, analyze,
and solve complex problems, it enables them to gain insights and make
informed decisions.
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