Matrices

Note

The two matrices are added cell by cell. The result is a new matrix; the inputs are unchanged.

Limits

Both matrices must have the same row and column counts; a size mismatch raises an error.

Note

Inserts the array as a column at the given position and increases the column count. If the matrix is empty (0 rows), the added column's length sets the row count.

Note

Inserts the array as a row at the given position and increases the row count. If the matrix is empty (0 columns), the first added row's length sets the column count.

When to use

To grow a matrix by adding rows bar by bar — an accumulating table of observations.

Note

Divides the sum by the cell count. Returns na (not 0) on an empty matrix; guard the result with na().

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Collects the column top to bottom into an array. The returned array is a copy; it does not affect the matrix.

When to use

To process all samples of a variable (a column) as an array — mean, max, standard deviation.

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Used as the loop bound over columns. matrixColumns is a second name for the same thing.

Note

Returns exactly the same result as matrixCols — an alternative name provided for readability.

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Performs a vertical stack (appends rows below). The result is a new matrix; the inputs are unchanged.

Limits

Both matrices must have the same column count; a mismatch raises an error.

Note

The copy is fully separate from the original; changing one does not affect the other. Used to experiment on a matrix without corrupting it.

Note

Computed by elimination with partial pivoting. A determinant of 0 means the matrix has no inverse (its rows/columns are dependent).

Limits

Defined only for a square matrix; returns na otherwise.

Note

If the second argument is a matrix, subtraction is done cell by cell; if it is a single number, that number is subtracted from all cells. The result is a new matrix.

Limits

When used with two matrices, the sizes must match; a mismatch raises an error.

Note

Computed by the Jacobi method for symmetric matrices. Eigenvalues give the matrix's diagonal magnitudes (its scale along the principal axes).

When to use

To extract principal components (dominant directions) from a covariance matrix — dimensionality reduction, risk concentration.

Limits

The method is for symmetric matrices; on a non-symmetric matrix the result is not meaningful. Verify with matrixIsSymmetric first.

Note

Computed by the Jacobi method for symmetric matrices; each column of the result matrix is an eigenvector, matching the order of matrixEigenvalues.

Limits

The method is for symmetric matrices; on a non-symmetric matrix the result is not meaningful. Verify with matrixIsSymmetric first.

Note

Useful to check whether a matrix is non-empty before feeding statistics functions (matrixAvg, matrixMedian).

Note

Does not change the size, it just overwrites the contents with a single value. A quick way to reset a matrix before reusing it.

When to use

To reset a whole matrix to a single value (often 0).

Note

Rows and columns start at 0. An out-of-range index does not crash, it yields na; you can check the result with na().

When to use

To read the value at a specific position. To take a whole row or column, use matrixRow/matrixCol.

Note

Computed by Gauss-Jordan elimination. Multiplying by the inverse yields the identity. A matrix with determinant 0 has no inverse; na is returned then.

Limits

Produces a result only for square, non-singular matrices; otherwise na. Guard the result with na() before using it in a product.

Note

The anti-diagonal runs from top-right to bottom-left; this check verifies that only that diagonal may be filled.

Note

In an antisymmetric matrix the diagonal is necessarily 0 (since m[i][i] = -m[i][i] holds only for 0).

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Used to validate structures that should contain only 0-1, such as an adjacency matrix.

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The diagonal values may be any number; the condition is only that the off-diagonal is 0.

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The identity is the neutral element in multiplication (m × identity = m). This check tells whether a matrix is the identity.

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Used as a guard before functions that require a square matrix (determinant, inverse, power, trace).

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This is a row-stochastic check; being square is not required, only that each row sums to 1. Used to validate transition (Markov) matrices.

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A symmetric matrix is a mirror across the diagonal. Covariance and correlation matrices are symmetric; the eigenvalue functions are designed for such matrices.

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In an upper-triangular matrix the area below the diagonal is zero, in a lower-triangular one the area above. Either case qualifies as triangular.

Note

Can be used to check whether a computation wrote any value into the matrix.

Note

Each cell of m1 is multiplied by all of m2 and placed block by block. The result grows to the product of both sizes.

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Compares all cells without distinguishing rows or columns.

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All cells are sorted and the middle value is taken. The median is less sensitive to outliers than the mean.

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Compares all cells without distinguishing rows or columns.

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When several values share the highest frequency, the smallest value is chosen (a stable, deterministic result).

Note

Matrix×matrix is true matrix multiplication (not element-wise): result[i][j] is the dot product of a's row i with b's column j. Matrix×array applies the same dot-product logic per row: result[i] is the dot product of a's row i with the array. Matrix×number is plain scalar multiplication.

Limits

a must always be the matrix — the order cannot be flipped even when b is a scalar or array (matrixMult(number, a) is not supported). The inner dimensions must match: for matrix×matrix, a's column count must equal b's row count; for matrix×array, a's column count must equal the array's length — otherwise it raises an error. The order matters (a×b ≠ b×a).

Note

A matrix is a two-dimensional grid of numbers made of rows and columns; every other matrix function expects an object built this way.

When to use

To allocate a fixed-size number grid before a computation — a weight table, a transition matrix, a covariance accumulator.

Note

Computed as (mᵀm)⁻¹mᵀ; it gives the least-squares solution for non-square or non-invertible matrices. For a square invertible matrix the result equals the ordinary inverse.

When to use

When solving over-determined (rows > columns) linear systems by least squares.

Limits

If the columns are dependent (mᵀm becomes singular) no result is produced and na is returned; guard the result with na().

Note

Multiplies the matrix by itself n times (not an ordinary numeric power). At n=0 the identity, at n=1 the matrix itself is returned.

Limits

Defined only for a square matrix; raises an error otherwise.

Note

Computed by elimination. If the rank is less than the row or column count, the matrix has dependency (redundancy) and no inverse.

Note

Deletes the column from the matrix (the column count drops by one) and returns that column as an array. Modifies in place.

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Deletes the row from the matrix (the row count drops by one) and returns that row as an array. Modifies in place.

Note

Cells are read row-major and poured into the new shape. If the new size is larger, missing cells become 0; if smaller, extra cells are dropped. Does not change the source.

Note

Reverses both the order of rows and the cells within each row; the first cell swaps with the last (a 180° rotation effect). Modifies in place.

Note

The returned array is a copy; modifying it does not affect the source matrix. An empty result reads as size 0 with arraySize.

When to use

To process all values of a row with array functions (arraySum, arrayAvg).

Note

Used to know the bound before looping over rows. For the column count use matrixCols.

Note

Overwrites an existing cell; it does not grow the matrix. If the index is out of range it silently does nothing. To add a new row/column use matrixAddRow/matrixAddCol.

When to use

To fill the cells of a matrix allocated with matrixNew one by one.

Note

Rows are reordered as whole units by the value in the chosen column (each row stays intact internally). Does nothing if the column index is invalid.

When to use

To rank rows by a criterion (e.g. a score column) — bringing the best/worst rows to the front.

Note

The end indices are exclusive (r2 and c2 are not included). Does not change the source; returns a copy of the sliced region.

When to use

To process a specific block (a window, a sub-table) of a large matrix separately.

Note

Sums all values without distinguishing rows or columns. Yields 0 for an empty matrix.

Note

Swaps two whole columns. Does nothing if either index is out of range.

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Swaps two whole rows. Does nothing if either index is out of range.

Note

For a non-square matrix it sums the diagonal up to the shorter side. The trace reduces the diagonal energy to a single number.

Note

Does not change the source, it returns a new matrix. Cell at row i, column j becomes row j, column i in the output.

When to use

To turn row vectors into column vectors, or to make dimensions fit for a product.