Submatrix Input for Simplified Matrix Calculation Display

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Solution Overview

Problem

Existing scientific calculators cannot efficiently learn or perform calculations using simplified matrix calculation formulas generated from combinations of submatrices, which are essential for efficient computation with large matrices.

Innovation Solution

A matrix calculation apparatus and method that includes a matrix calculation formula display controller, a submatrix receiver, and a matrix size change display controller, allowing users to input submatrices into a matrix calculation formula and dynamically change the matrix size based on the submatrix, enabling the display and calculation of simplified formulas using submatrices.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Ease of operation

If scientific calculators display matrix calculation formulas with full matrix elements, then calculation results can be obtained, but the complexity of the display increases and efficiency of learning simplified calculations deteriorates

Engineering Contradiction:

Improveease of learning simplified matrix calculationsVSAvoidcomplexity of matrix formula display

Core Design Contradiction:

Ease of operationVSDevice complexity

Solution Approach 1:

The patent divides large matrices into smaller submatrices (e.g., dividing a 4x4 matrix into four 2x2 submatrices). This segmentation allows the calculator to display and process matrix calculations in a simplified, modular manner, making it easier to learn and understand while reducing the visual complexity of the formulas.

Inventive Principle:

Principle #1Segmentation

Solution Approach 2:

The patent implements dynamic display adjustment where the calculator can switch between displaying full matrix elements and simplified submatrix representations. The display dynamically adapts based on the calculation context, showing detailed views when needed and simplified views for learning efficient calculation procedures.

Inventive Principle:

Principle #15Dynamics

2Productivity

If scientific calculators perform standard matrix multiplication, then calculation results are obtained, but the time required to learn efficient calculation procedures with submatrices increases

Engineering Contradiction:

Improveefficiency of matrix calculationVSAvoidtime required to learn simplified calculation procedures

Core Design Contradiction:

ProductivityVSLoss of time

Solution Approach 1:

The patent pre-configures the calculator with submatrix division capabilities and simplified calculation procedures before the user needs to perform calculations. The calculator automatically divides matrices into submatrices and presents simplified calculation formulas, allowing users to learn and apply efficient procedures without time-consuming manual setup.

Inventive Principle:

Principle #10Preliminary action

Solution Approach 2:

The patent incorporates feedback mechanisms where the calculator displays the simplified submatrix calculation procedures and allows users to verify each step. This feedback loop enables users to learn efficient calculation methods by observing and interacting with the step-by-step simplification process, reducing the time needed to master these procedures.

Inventive Principle:

Principle #23Feedback

3Measurement precision

If scientific calculators display detailed matrix elements, then calculation accuracy is maintained, but the ability to simplify and learn efficient calculation procedures deteriorates

Engineering Contradiction:

Improveaccuracy of matrix calculationVSAvoidability to simplify matrix calculations

Core Design Contradiction:

Measurement precisionVSAdaptability or versatility

Solution Approach 1:

The patent makes the calculator universally applicable by enabling it to perform both standard detailed matrix multiplication and simplified submatrix calculations. The same calculator can adapt to different learning needs and calculation requirements, providing detailed views for accuracy-critical operations and simplified views for learning efficient procedures.

Inventive Principle:

Principle #6Universality (Multi-functionality)

Solution Approach 2:

The patent changes the display and calculation parameters dynamically based on the operation mode. When in simplified mode, the calculator uses submatrix representations and adjusted calculation parameters to enable learning of efficient procedures. When in detailed mode, it uses full matrix elements to maintain calculation accuracy, thus adapting to different user needs.

Inventive Principle:

Principle #35Parameter changes

Data Source

PatentUS9645973B2Matrix calculation apparatus, matrix calculation method, and computer readable medium having matrix calculation process program stored thereon

Publication Date: 2017.05.09 CASIO COMPUTER CO LTD

AI summary

There is provided a matrix calculation apparatus. The apparatus includes: a matrix calculation formula display controller configured to display a matrix calculation formula on a display unit, wherein the matrix calculation formula comprises a first matrix; a matrix display controller configured to display a second matrix on the display unit; a submatrix receiver configured to input the second matrix into a certain element of the first matrix as a submatrix of the first matrix in response to a user operation; and a matrix size change display controller configured to change a size of the first matrix in accordance with a size of the second matrix and the certain element of the first matrix into which the second matrix is input and then display the matrix calculation formula.