# Linear Algebra

Linear algebra is the branch of mathematics concerning vector spaces and linear mappings between such spaces. Linear algebra is central to both pure and applied mathematics.

Provided below is a list of all the matrix operations and decompositions available in Mintoris Basic.

### d = MatDet(a())

- Compute the matrix determinate.

### c = MatCond(a())

- Ratio of largest to smallest singular value.

### r = MatRank(a())

- Effective numerical rank, obtained from SVD.

### n = MatNorm1(a())

- Maximum column sum.

### n = MatNorm2(a())

- Maximum singular value.

### n = MatNormF(a())

- Square root of the sum of squares of all elements.

### n = MatNormInf(a())

- Maximum row sum.

### t = MatTrace(a())

- Sum of the diagonal elements.

- Add two matrices. C = A + B

### c() = MatSub(a(),b())

- Subtract two matrices. C = A - B

### c() = MatMult(a(),b())

- Linear algebraic matrix multiplication. C = A * B

### c() = MatSolve(a(),b())

- Solve A*X = B. Solution if A is square, least squares solution otherwise.

### c() = MatUMinus(a())

- Unary minus. C = -A

### c() = MatRandom(rows, cols)

- Generate matrix with random elements.

### c() = MatInverse(a())

- Inverse A if A is square, pseudoinverse otherwise.

### c() = MatIdentity(rows, cols)

- Returns an m-by-n matrix with ones on the diagonal and zeros elsewhere.

### c() = MatTranspose(a())

- Matrix transpose.

### c() = MatSolveTranspose(a())

- Solve X*A = B, which is also A'*X' = B'