To find the size of a matrix put it on the stack,
type SIZE and press [ENTER].

Example:
[[ 1 2 3]
[2 2 2 ]]
SIZE

Result: size {2 3}
A matrix with 2 lines and 3 colums.

Subtracts matrices

You can only subtracts matrices with the same size.
If sizes are different it will returns invalid dimension error

Example:
Subtract a matrix in level 1 from a matrix in level 2

[ [2 3] [5 1] ]
[ [4 6] [3 2] ]


Result:

[ [-2 -3]
[ 2 -1] ]


3)    x

---

Multiplies Matrices

You can Multiply matrices with compatible size.
An invalid dimension error will be displayed
at status area if the size is not compatible.

We know from Math that a matrix A {lines-a columns-a}
just can be multiplyed by a matrix B {lines-b columns-b}
if the numbers of columns of A is equal the numbers of lines of B,

i.e. columns-a = lines-b .

The new matrix will have size:
{lines-a columns-b}

Example:

[[1 2 3][4 5 6]]           size {2 3}    ( 2 lines x 3 columns matrix )
[[1 4][2 5][3 6]]           size {3 2}    ( 3 lines x 2 columns matrix )
x

Result:
[ [14 32]
   [32 77] ]

size {2 2}

Divide matrices

You can only divide a square matrix by other of the same order.
To divide square matrices put both square matrices
on the stack and press


Example:

Divede the matrices:
[[1 2 ][4 5 ]] size {2 2}
[[1 4][2 5]] size {2 2}

In HP calculator:

[ [1 2 ] [4 5 ] ]
[ [1 4] [2 5] ]


Result:
[[ 3.66666... 3.333333...]
[ -.66666... -.333333...]]

It is the same that
[ [1 2 ][4 5 ] ]
[ [1 4][2 5] ]
[ 1/X ] [SWAP] x

Multiplies a Matrix by a constant

Put the matrix in level 2
and the constant in level 1
and press x.

Example:

[[1 2 ][4 5 ]]
5
x

Result:
[ [5 10]
 [20 25] ]

The same is also valid for

Example:

[ [1 2 ] [4 5 ] ]
5


Result:
[ [.2 .4]
 [.8 1] ]


6) 1 / X

---

Inver Matrices

To invert a matrix it must

1- be a square matrix.
3- have determinant different of zero.

To invert the matrix put it on the stack an press [1/X]

Example:

[ [5 2 ] [4 8] ]
[1/X]

Result:
[ [.25 -.0625]
  [-.125 .15625] ]

Calculates the determinant of a matrix

You just can calculate determinant of a square matrices.
To calculate the determinant put the matrix on the stack,
type DET and press [ENTER].

Example:

[ [4 5 6][9 6 3][-5 8 7] ]
DET
[ENTER]

Result: 294

Transpose a Matrix

TRN change lines for colums, i.e. transpose a matrix.

Example:

[ [1 2 3 ] [4 5 6] ]
TRN

Result:
[ [1 4 ]
  [2 5]
  [3 6] ]

Generates a Random matrix

Example:

{2 3}
RANM

Result:
[ [-1 0 7]
 [2 -9 -4] ]

Note: the random matrix generated can be, of course,
numericaly different of the one in this example.

Creates an Identity matrix

Example:

3
IDN

Result:
[ [1 0 0]
 [0 1 0]
 [0 0 1] ]

Trace calculate the sum of the main diagonal
of a square matrix.

Example:

[ [4 8 9]
 [3 6 7]
 [2 3 5] ]
TRACE

Result:15

Power of a matrix

You can calculate the result of the matrix A
at the power n using [ENTER] and x

Example:

On the stack type,

[[4 8 9]  [3 6 7]  [2 3 5]]

Pressing [ENTER] three times you will get:

[ [4 8 9]
  [3 6 7]
  [2 3 5] ]

[ [4 8 9]
  [3 6 7]
  [2 3 5] ]

[ [4 8 9]
  [3 6 7]
  [2 3 5] ]

Press now two times x

Result:
[ [827 1517 1956]
 [627 1150 1483]
 [383 702 906] ]
That is the matrix at the 3rd power.