Enter ten ordered pairs. Review matrix properties with ease. Export clean results for clear records. Compare columns and trends with simple detailed steps today.
Enter all twenty values. Each row contains one ordered pair.
This table shows sample rows and common row calculations.
| Row | Column 1 | Column 2 | Row Sum | Row Length |
|---|---|---|---|---|
| 1 | 2 | 5 | 7 | 5.3852 |
| 2 | 4 | 9 | 13 | 9.8489 |
| 3 | 6 | 13 | 19 | 14.3178 |
| 4 | 8 | 17 | 25 | 18.7883 |
| 5 | 10 | 21 | 31 | 23.2594 |
| 6 | 12 | 25 | 37 | 27.7308 |
| 7 | 14 | 29 | 43 | 32.2025 |
| 8 | 16 | 33 | 49 | 36.6742 |
| 9 | 18 | 37 | 55 | 41.1461 |
| 10 | 20 | 41 | 61 | 45.618 |
Matrix form: A is a 10 x 2 matrix with rows [x, y].
Row sum: s = x + y.
Row difference: d = y - x.
Row product: p = x multiplied by y.
Row length: L = square root of x squared plus y squared.
Column mean: mean = column sum divided by 10.
Sample variance: variance = sum of squared deviations divided by 9.
Sample standard deviation: standard deviation = square root of sample variance.
Dot product: x dot y = sum of each x value multiplied by its paired y value.
Covariance: covariance = sum of paired deviations divided by 9.
Correlation: correlation = covariance divided by both sample standard deviations.
Cosine similarity: cosine = dot product divided by the product of both column norms.
Frobenius norm: norm = square root of the sum of every entry squared.
Rank check: rank is estimated from the determinant of A transposed times A.
Linear regression: y = slope x + intercept.
Scalar transform: transformed value = scalar multiplied by value plus shift.
A 10 x 2 matrix is useful when each record has two related values. Many school and practical tasks use this structure. It can represent points, paired scores, paired costs, coordinates, samples, or measurements from two columns. This calculator turns those ten pairs into clear matrix information.
The tool keeps the workflow simple. You enter twenty values, arranged as ten rows and two columns. Then it reports row sums, row differences, products, lengths, column totals, means, variances, standard deviations, and matrix measures. It also prepares transformed values using a scalar multiplier and an added shift. This helps when a teacher asks for scaled data or adjusted observations.
The column comparison area is important. It checks the dot product, covariance, correlation, cosine similarity, and regression line. These results show whether the two columns move together. A positive correlation shows similar direction. A negative correlation shows opposite direction. A value near zero suggests weak linear connection.
The rank check gives structural insight. A rank of two means the two columns are not simple multiples. A rank of one means one column follows the other by scaling, or only one useful direction exists. A rank of zero means every entry is zero. This is helpful before solving linear models or checking data quality.
The calculator also supports reporting. CSV export is useful for spreadsheets. PDF export is useful for assignments, notes, and records. The example table shows how rows are evaluated. You can compare your entries with the sample output before submitting your own numbers.
Use consistent units when entering values. Do not mix centimeters with meters in the same column unless you convert them first. Very large and very small values can affect rounding. Select suitable decimals for readable output. Use more decimals for statistics, regression, and covariance.
This calculator does not replace mathematical reasoning. It speeds repeated arithmetic and reduces copying mistakes. Always review formulas and inputs. Matrix work becomes easier when values, row behavior, and column relationships are visible together. Practice one row change, then compare totals, norms, rank, and relationships again carefully.
It is a matrix with ten rows and two columns. Each row has two related values. It can represent ordered pairs, paired measurements, score pairs, coordinates, or two-variable observations.
Yes. The calculator accepts positive numbers, negative numbers, decimals, and zero. Negative values are useful for coordinates, deviations, balances, and signed measurements.
Rank shows how many independent column directions exist. Rank two means both columns add separate information. Rank one means the columns are dependent. Rank zero means all entries are zero.
It is the square root of the sum of every matrix entry squared. It gives one size measure for the whole 10 x 2 matrix.
Correlation shows the linear relationship between both columns. Positive values show similar movement. Negative values show opposite movement. Values near zero suggest weak linear connection.
Covariance shows whether both columns vary together. It keeps original unit influence, so it is useful before reviewing standardized correlation.
It multiplies each original value by your scalar, then adds your shift. This helps create adjusted, scaled, or converted matrix values.
Yes. After calculation, use the CSV button for spreadsheet records. Use the PDF button for a printable summary of main results and row values.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.